From fe053543f133318dff1191aec5ebca74f368fa57 Mon Sep 17 00:00:00 2001 From: tkoz0 <13438573+tkoz0@users.noreply.github.com> Date: Mon, 2 Dec 2024 08:33:01 -0500 Subject: [PATCH] table css refactor --- academic/misc/2024-math-calendar.html | 24 ++-- academic/misc/2024-math-calendar/01-jan.html | 6 +- academic/misc/2024-math-calendar/02-feb.html | 2 +- academic/misc/2024-math-calendar/03-mar.html | 2 +- academic/misc/2024-math-calendar/04-apr.html | 20 +-- academic/misc/2024-math-calendar/05-may.html | 2 +- academic/misc/2024-math-calendar/06-jun.html | 26 ++-- academic/misc/2024-math-calendar/07-jul.html | 2 +- academic/misc/2024-math-calendar/08-aug.html | 4 +- academic/misc/2024-math-calendar/09-sep.html | 10 +- academic/misc/2024-math-calendar/10-oct.html | 2 +- academic/misc/2024-math-calendar/11-nov.html | 2 +- academic/misc/2024-math-calendar/12-dec.html | 114 +++++++++++++++++- academic/misc/20240302-power-sum.html | 4 +- .../misc/20240323-some-putnam-problems.html | 2 +- academic/proj_euler/part0001.html | 20 +-- academic/proj_euler/part0011.html | 26 ++-- academic/proj_euler/part0021.html | 22 ++-- academic/proj_euler/part0031.html | 22 ++-- academic/proj_euler/part0041.html | 20 +-- mathstyles.css | 10 +- 21 files changed, 231 insertions(+), 111 deletions(-) diff --git a/academic/misc/2024-math-calendar.html b/academic/misc/2024-math-calendar.html index 1aa1f19..86adc42 100644 --- a/academic/misc/2024-math-calendar.html +++ b/academic/misc/2024-math-calendar.html @@ -34,7 +34,7 @@

Math Calendar 2024

- +
@@ -93,7 +93,7 @@

Math Calendar 2024

January
MoTuWeThFrSaSu
- +
@@ -152,7 +152,7 @@

Math Calendar 2024

February
MoTuWeThFrSaSu
- +
@@ -211,7 +211,7 @@

Math Calendar 2024

March
MoTuWeThFrSaSu
- +
@@ -270,7 +270,7 @@

Math Calendar 2024

April
MoTuWeThFrSaSu
- +
@@ -329,7 +329,7 @@

Math Calendar 2024

May
MoTuWeThFrSaSu
- +
@@ -388,7 +388,7 @@

Math Calendar 2024

June
MoTuWeThFrSaSu
- +
@@ -447,7 +447,7 @@

Math Calendar 2024

July
MoTuWeThFrSaSu
- +
@@ -506,7 +506,7 @@

Math Calendar 2024

August
MoTuWeThFrSaSu
- +
@@ -565,7 +565,7 @@

Math Calendar 2024

September
MoTuWeThFrSaSu
- +
@@ -624,7 +624,7 @@

Math Calendar 2024

October
MoTuWeThFrSaSu
- +
@@ -683,7 +683,7 @@

Math Calendar 2024

November
MoTuWeThFrSaSu
- +
diff --git a/academic/misc/2024-math-calendar/01-jan.html b/academic/misc/2024-math-calendar/01-jan.html index b03b545..2b44a60 100644 --- a/academic/misc/2024-math-calendar/01-jan.html +++ b/academic/misc/2024-math-calendar/01-jan.html @@ -20,7 +20,7 @@

Math Calendar 2024 January

-
December
MoTuWeThFrSaSu
+
@@ -1393,7 +1393,7 @@

Jan 25

work is summarized in the table below.

-
January
MoTuWeThFrSaSu
+
@@ -1439,7 +1439,7 @@

Jan 25

this and the work is summarized in the following table.

-
step compute this
+
diff --git a/academic/misc/2024-math-calendar/02-feb.html b/academic/misc/2024-math-calendar/02-feb.html index bb312aa..42005d2 100644 --- a/academic/misc/2024-math-calendar/02-feb.html +++ b/academic/misc/2024-math-calendar/02-feb.html @@ -20,7 +20,7 @@

Math Calendar 2024 February

-
step compute this
+
diff --git a/academic/misc/2024-math-calendar/03-mar.html b/academic/misc/2024-math-calendar/03-mar.html index 870adaa..feb4c48 100644 --- a/academic/misc/2024-math-calendar/03-mar.html +++ b/academic/misc/2024-math-calendar/03-mar.html @@ -20,7 +20,7 @@

Math Calendar 2024 March

-
February
MoTuWeThFrSaSu
+
diff --git a/academic/misc/2024-math-calendar/04-apr.html b/academic/misc/2024-math-calendar/04-apr.html index 33fbc4c..82f2f4b 100644 --- a/academic/misc/2024-math-calendar/04-apr.html +++ b/academic/misc/2024-math-calendar/04-apr.html @@ -13,6 +13,8 @@ width: 250px; text-align: center; } + .r { background: #f77; } + .g { background: #7f7; } @@ -20,7 +22,7 @@

Math Calendar 2024 April

-
March
MoTuWeThFrSaSu
+
@@ -157,13 +159,13 @@

Apr 05

5 cases of congruency modulo 10.

-
April
MoTuWeThFrSaSu
+
- - - - - + + + + +
\(\mod10\)\(p^2-1\)\(p^2+1\)
102
380
546
780
902
102
380
546
780
902

@@ -930,7 +932,7 @@

Apr 29

summarizes the steps which does involve a few tedious calculations.

- +
@@ -943,7 +945,7 @@

Apr 29

Below is a similar table.

-
\(k\)\(a_k\)\(f(a_k)\)\(3^{-1}\)\(a_{k+1}\)
\(1\)\(0\)\(16\equiv0\mod4\)Not needed\(0-16\cdot3^{-1}\equiv0\mod4\)
\(2\)\(0\)\(16\equiv0\mod8\)Not needed\(0-16\cdot3^{-1}\equiv0\mod8\)
+
diff --git a/academic/misc/2024-math-calendar/05-may.html b/academic/misc/2024-math-calendar/05-may.html index 48587cb..168e81a 100644 --- a/academic/misc/2024-math-calendar/05-may.html +++ b/academic/misc/2024-math-calendar/05-may.html @@ -20,7 +20,7 @@

Math Calendar 2024 May

-
\(k\)\(a_k\)\(f(a_k)\)\(5^{-1}\)\(a_{k+1}\)
\(1\)\(1\)\(20\equiv0\mod4\)Not needed\(1-20\cdot5^{-1}\equiv1\mod4\)
\(2\)\(1\)\(20\equiv4\mod8\)\(5\mod8\)\(1-20\cdot5^{-1}\equiv5\mod8\)
+
diff --git a/academic/misc/2024-math-calendar/06-jun.html b/academic/misc/2024-math-calendar/06-jun.html index 2225590..b4960a3 100644 --- a/academic/misc/2024-math-calendar/06-jun.html +++ b/academic/misc/2024-math-calendar/06-jun.html @@ -13,6 +13,8 @@ width: 250px; text-align: center; } + .r { background: #f77; } + .g { background: #7f7; } @@ -20,7 +22,7 @@

Math Calendar 2024 June

-
May
MoTuWeThFrSaSu
+
@@ -331,17 +333,17 @@

Jun 15

starting entirely in green and then marking composite numbers in red.

-
June
MoTuWeThFrSaSu
- - - - - - - - - - +
23456789
10111213141516171819
20212223242526272829
30313233343536373839
40414243444546474849
50515253545556575859
60616263646566676869
70717273747576777879
80818283848586878889
90919293949596979899
+ + + + + + + + + +
23456789
10111213141516171819
20212223242526272829
30313233343536373839
40414243444546474849
50515253545556575859
60616263646566676869
70717273747576777879
80818283848586878889
90919293949596979899

diff --git a/academic/misc/2024-math-calendar/07-jul.html b/academic/misc/2024-math-calendar/07-jul.html index c3ac00f..3059965 100644 --- a/academic/misc/2024-math-calendar/07-jul.html +++ b/academic/misc/2024-math-calendar/07-jul.html @@ -20,7 +20,7 @@

Math Calendar 2024 July

- +
diff --git a/academic/misc/2024-math-calendar/08-aug.html b/academic/misc/2024-math-calendar/08-aug.html index f981351..2557a42 100644 --- a/academic/misc/2024-math-calendar/08-aug.html +++ b/academic/misc/2024-math-calendar/08-aug.html @@ -20,7 +20,7 @@

Math Calendar 2024 August

-
July
MoTuWeThFrSaSu
+
@@ -503,7 +503,7 @@

Aug 22

We can fill in the following table going row by row using the recurrence.

-
August
MoTuWeThFrSaSu
+
diff --git a/academic/misc/2024-math-calendar/09-sep.html b/academic/misc/2024-math-calendar/09-sep.html index a842de7..1fb9977 100644 --- a/academic/misc/2024-math-calendar/09-sep.html +++ b/academic/misc/2024-math-calendar/09-sep.html @@ -13,6 +13,8 @@ width: 250px; text-align: center; } + .r { background: #f77; } + .g { background: #7f7; } @@ -20,7 +22,7 @@

Math Calendar 2024 September

-
\(n\textbackslash i\)12345678
111111111
212222222
+
@@ -468,7 +470,7 @@

Sep 27

this to select from all possible cases found by considering divisors of 140.

-
September
MoTuWeThFrSaSu
+
@@ -489,7 +491,7 @@

Sep 27

- + @@ -524,7 +526,7 @@

Sep 27

- + diff --git a/academic/misc/2024-math-calendar/10-oct.html b/academic/misc/2024-math-calendar/10-oct.html index f6e9b6f..6300780 100644 --- a/academic/misc/2024-math-calendar/10-oct.html +++ b/academic/misc/2024-math-calendar/10-oct.html @@ -20,7 +20,7 @@

Math Calendar 2024 October

-
\(c+a\) \(b+c\) \(70\) \(3\)
\(2\) \(70\) \(13\) \(6\)
\(10\) \(14\)
+
diff --git a/academic/misc/2024-math-calendar/11-nov.html b/academic/misc/2024-math-calendar/11-nov.html index 78addb1..ce1174b 100644 --- a/academic/misc/2024-math-calendar/11-nov.html +++ b/academic/misc/2024-math-calendar/11-nov.html @@ -20,7 +20,7 @@

Math Calendar 2024 November

-
October
MoTuWeThFrSaSu
+
diff --git a/academic/misc/2024-math-calendar/12-dec.html b/academic/misc/2024-math-calendar/12-dec.html index db6756b..56097db 100644 --- a/academic/misc/2024-math-calendar/12-dec.html +++ b/academic/misc/2024-math-calendar/12-dec.html @@ -13,6 +13,9 @@ width: 250px; text-align: center; } + .b1 { border-top: 1px solid black; } + .b2 { border-left: 1px solid black; } + .td2 td { padding: 4px; text-align: center; } @@ -20,7 +23,7 @@

Math Calendar 2024 December

-
November
MoTuWeThFrSaSu
+
@@ -81,8 +84,117 @@

Math Calendar 2024 December

Dec 01

+

+Find \(-ijk\) where \(i,j,k\) are quaternions. +

+ +

+Quaternions are an extension of complex numbers which is not commutative, but it +is associative. Multiplication is defined where \(1\) is the identity element +and the imaginary basis products are +\[i^2=j^2=k^2=-1,\ ij=-ji=k,\ jk=-kj=i,\ ki=-ik=j\] +So by using this +\[-ijk=-(ij)k=-(k)k=-k^2=-(-1)=1\] +

+

Dec 02

+

+Find the remainder whehn \(x^6+1\) is divided by \(x^2-x+1\). +

+ +

+The most clear way to solve this would be to use polynomial division. +

+ +
December
MoTuWeThFrSaSu
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
\(x^4\)\(+x^3\)\(+0x^2\)\(-x\)\(-1\)
\(x^2\)\(-x\)\(+1\)\(x^6\)\(+0x^5\)\(+0x^4\)\(+0x^3\)\(+0x^2\)\(+0x\)\(+1\)
\(-\)\((x^6\)\(-x^5\)\(+x^4)\)
\(x^5\)\(-x^4\)\(+0x^3\)
\(-\)\((x^5\)\(-x^4\)\(+x^3)\)
\(-x^3\)\(+0x^2\)\(+0x\)
\(-\)\((-x^3\)\(+x^2\)\(-x)\)
\(-x^2\)\(+x\)\(+1\)
\(-\)\((-x^2\)\(+x\)\(-1)\)
\(2\)
+ +

+This shows that the remainder is \(2\) and +\[{x^6+1\over x^2-x+1}=x^4+x^3-x-1+{2\over x^2-x+1}\] +One other possible way to see it for this problem is noticing that \(x^2-x+1\) +is a factor of \(x^3+1\). Then \((x^3+1)(x^3-1)=x^6-1\) and adding the remainder +of \(2\) shows that \(x^6+1=(x^6-1)+2\) where \(x^2-x+1\) is a factor of +\(x^6-1\). Or it can also be found by seeing how to factor +\[x^6-1=(x^3+1)(x^3-1)=(x+1)(x^2-x+1)(x-1)(x^2+x+1)\] +

+

Dec 03

Dec 04

diff --git a/academic/misc/20240302-power-sum.html b/academic/misc/20240302-power-sum.html index e31d3b5..f1c868e 100644 --- a/academic/misc/20240302-power-sum.html +++ b/academic/misc/20240302-power-sum.html @@ -53,7 +53,7 @@

Double Summation Method

of \(p-1\) powers. To see how we can do this, consider a table like below.

- +
@@ -243,7 +243,7 @@

Matrix Methods

corresponds to a row and each \(j\) corresponds to a column.

-
\(1^{p-1}\)
\(2^{p-1}\)\(2^{p-1}\)
\(3^{p-1}\)\(3^{p-1}\)\(3^{p-1}\)
+
diff --git a/academic/misc/20240323-some-putnam-problems.html b/academic/misc/20240323-some-putnam-problems.html index e273e7e..4476dda 100644 --- a/academic/misc/20240323-some-putnam-problems.html +++ b/academic/misc/20240323-some-putnam-problems.html @@ -38,7 +38,7 @@

Area in 2D Plane

following inequalities:

-
\(c_1{1\choose0}\)\(c_1{1\choose1}n\)
\(c_2{2\choose0}\)\(c_2{2\choose1}n\)
+
diff --git a/academic/proj_euler/part0001.html b/academic/proj_euler/part0001.html index 0874e5a..0c0b3a5 100644 --- a/academic/proj_euler/part0001.html +++ b/academic/proj_euler/part0001.html @@ -71,7 +71,7 @@

Problem 1

1000 so we should not count 1000.

-
Answer:233168
+
Answer:233168

Problem 2

@@ -138,7 +138,7 @@

Problem 2

Note: the largest term included in the sum is \(F_{33}=3524578\).

-
Answer:4613732
+
Answer:4613732

Problem 3

@@ -179,7 +179,7 @@

Problem 3

numbers.

-
Answer:6857
+
Answer:6857
The factorization is \(71\cdot839\cdot1471\cdot6857\)

Problem 4

@@ -236,7 +236,7 @@

Problem 4

print(largest) -
Answer:906609
+
Answer:906609
The product is \(993\cdot913\)

Problem 5

@@ -316,7 +316,7 @@

Problem 5

print(result) -
Answer:232792560
+
Answer:232792560
The factorization is: \(2^4\cdot3^2\cdot5\cdot7\cdot11\cdot13\cdot17\cdot19\)
@@ -363,7 +363,7 @@

Problem 6

expected, the solution expression is also asymptotic to \(N^4/4\).

-
Answer:25164150
+
Answer:25164150

Problem 7

@@ -516,7 +516,7 @@

Problem 7

Note: the sieve size calculated to use is 116684, about 11% overestimated.

-
Answer:104743
+
Answer:104743

Problem 8

@@ -646,7 +646,7 @@

Problem 8

print(largest) -
Answer:23514624000
+
Answer:23514624000
The consecutive digits forming this product are: 5576689664895 (starts with the last 3 digits on the 4th line)
@@ -735,7 +735,7 @@

Problem 9

print(a*b*c * d**3) -
Answer:31875000
+
Answer:31875000
The triple is (200,375,425), 25 times the primitive triple (8,15,17)

Problem 10

@@ -788,7 +788,7 @@

Problem 10

Note: a total of 148933 primes are summed.

-
Answer:142913828922
+
Answer:142913828922
diff --git a/academic/proj_euler/part0011.html b/academic/proj_euler/part0011.html index 8f848a5..187c39f 100644 --- a/academic/proj_euler/part0011.html +++ b/academic/proj_euler/part0011.html @@ -136,7 +136,7 @@

Problem 11

print(f'start at {sol_rc} going {sol_dir} multiply {sol_nums}') -
Answer:70600674
+
Answer:70600674
Product is \(87\cdot97\cdot94\cdot89\) (starting in the 16th row and 4th column, going along the up-right diagonal)
@@ -216,7 +216,7 @@

Problem 12

n += 1 -
Answer:76576500
+
Answer:76576500
The factorization is \(2^2\cdot3^2\cdot5^3\cdot7\cdot11\cdot13\cdot17\) and it has \(3\cdot3\cdot4\cdot2\cdot2\cdot2\cdot2=576\) divisors
@@ -570,7 +570,7 @@

Problem 13

print(''.join(map(str,total[:10]))) -
Answer:5537376230
+
Answer:5537376230

Problem 14

@@ -637,7 +637,7 @@

Problem 14

integers.

-
Answer:837799
+
Answer:837799

Problem 15

@@ -714,7 +714,7 @@

Problem 15

Note: the solution does not fit in a 32 bit integer.

-
Answer:137846528820
+
Answer:137846528820

Problem 16

@@ -750,7 +750,7 @@

Problem 16

print(sum(number)) -
Answer:1366
+
Answer:1366

Problem 17

@@ -814,7 +814,7 @@

Problem 17

-
QuadrantInequality
I: \(x\geq0,y\geq0\)\(y\geq x-1\)
II: \(x<0,y\geq0\)\(y\geq-x-1\)
+
@@ -827,7 +827,7 @@

Problem 17

numberword formlength
1one3
2two3
9nine4
total36
- +
@@ -848,7 +848,7 @@

Problem 17

word like "twenty" which is used 10 times and each number 1-9.

-
numberword formlength
10ten3
11eleven6
+
@@ -873,7 +873,7 @@

Problem 17

adding all these together, we get the answer.

-
Answer:21124
+
Answer:21124

Problem 18

@@ -950,7 +950,7 @@

Problem 18

print(largestsum) -
Answer:1074
The path is: +
Answer:1074
The path is: 75, 64, 82, 87, 82, 75, 73, 28, 83, 32, 91, 78, 58, 73, 93

Problem 19

@@ -991,7 +991,7 @@

Problem 19

print(count) -
Answer:171
+
Answer:171

Problem 20

@@ -1032,7 +1032,7 @@

Problem 20

print(sum(num)) -
Answer:648
+
Answer:648
diff --git a/academic/proj_euler/part0021.html b/academic/proj_euler/part0021.html index a4a6491..0a1534b 100644 --- a/academic/proj_euler/part0021.html +++ b/academic/proj_euler/part0021.html @@ -111,7 +111,7 @@

Problem 21

print(total) -
Answer:31626
+
Answer:31626
The amicable pairs are (220,284), (1184,1210), (2620,2924), (5020,5564), (6232,6368)
@@ -148,7 +148,7 @@

Problem 22

print(sum((i+1)*name_value(name) for i,name in enumerate(data))) -
Answer:871198282
+
Answer:871198282

Problem 23

@@ -221,7 +221,7 @@

Problem 23

Wikipedia.

-
Answer:4179871
+
Answer:4179871

Problem 24

@@ -344,7 +344,7 @@

Problem 24

\(2\times9!+7\times8!\). Below is a table showing the work:

-
tens wordlengthletters used
twenty610×6 + 36 = 96
thirty610×6 + 36 = 96
+
@@ -424,7 +424,7 @@

Problem 24

remaining digits) factorial to take.

-
Answer:2783915460
+
Answer:2783915460

Problem 25

@@ -507,7 +507,7 @@

Problem 25

number of digits in these numbers.

-
Answer:4782
+
Answer:4782

Problem 26

@@ -571,7 +571,7 @@

Problem 26

print(num) -
Answer:983
+
Answer:983
The cycle length is 982

Problem 27

@@ -657,7 +657,7 @@

Problem 27

print(amax*bmax) -
Answer:-59231
+
Answer:-59231
The function is \(f(n)=n^2-61x+971\)

Problem 28

@@ -715,7 +715,7 @@

Problem 28

=1+\frac{S}{3}(16S^2+30S+26) \end{align}\] -
Answer:669171001
+
Answer:669171001

Problem 29

@@ -771,7 +771,7 @@

Problem 29

counting it for the representation with the smallest base.

-
Answer:9183
+
Answer:9183

Problem 30

@@ -801,7 +801,7 @@

Problem 30

print(total) -
Answer:443839
+
Answer:443839
The numbers are 4150, 4151, 54748, 92727, 93084, 194979
diff --git a/academic/proj_euler/part0031.html b/academic/proj_euler/part0031.html index ff12e56..010de22 100644 --- a/academic/proj_euler/part0031.html +++ b/academic/proj_euler/part0031.html @@ -107,7 +107,7 @@

Problem 31

print(W[P]) -
Answer:73682
+
Answer:73682

Problem 32

@@ -141,7 +141,7 @@

Problem 32

print(sum(c_set)) -
Answer:45228
+
Answer:45228
The product identities are: 
 4 * 1738 = 6952
@@ -201,7 +201,7 @@ 
Problem 33

 print(product.denominator)
-
Answer:100
+
Answer:100
The 4 fractions are: 16/64, 19/95, 26/65, 49/98 which simplify to 1/4, 1/5, 2/5, 1/2 and multiply to 1/100
@@ -241,7 +241,7 @@

Problem 34

print(total) -
Answer:40730
+
Answer:40730
There are only 2 such numbers: 145, 40585

Problem 35

@@ -318,7 +318,7 @@

Problem 35

print(len(circulars)) -
Answer:55
+
Answer:55
Full list: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 197, 199, 311, 337, 373, 719, 733, 919, 971, 991, 1193, 1931, 3119, 3779, 7793, 7937, 9311, 9377, 11939, 19391, 19937, 37199, 39119, 71993, @@ -385,7 +385,7 @@

Problem 36

print(total) -
Answer:872187
+
Answer:872187
The double palindromes: 1, 3, 5, 7, 9, 33, 99, 313, 585, 717, 7447, 9009, 15351, 32223, 39993, 53235, 53835, 73737, 585585
@@ -458,7 +458,7 @@

Problem 37

print(sum(lrtrunc)) -
Answer:748317
+
Answer:748317
Prime list: 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397

Problem 38

@@ -490,7 +490,7 @@

Problem 38

print(largest) -
Answer:932718654
+
Answer:932718654
All starting numbers: 1, 9, 192, 219, 273, 327, 6729, 6792, 6927, 7269, 7293, 7329, 7692, 7923, 7932, 9267, 9273, 9327
@@ -548,7 +548,7 @@

Problem 39

print(maxp[0]) -
Answer:840
+
Answer:840
There are 8 solutions for perimeter 840

Problem 40

@@ -568,7 +568,7 @@

Problem 40

showing the work:

-
step digit chosen
+
@@ -661,7 +661,7 @@

Problem 40

print(prod) -
Answer:210
+
Answer:210
The 7 digits multiplied are: 1, 1, 5, 3, 7, 2, 1
diff --git a/academic/proj_euler/part0041.html b/academic/proj_euler/part0041.html index 8967148..5d00c1e 100644 --- a/academic/proj_euler/part0041.html +++ b/academic/proj_euler/part0041.html @@ -84,7 +84,7 @@

Problem 41

primes.

-
Answer:7652413
+
Answer:7652413

Problem 42

@@ -128,7 +128,7 @@

Problem 42

print(sum(1 for x in data if triangle(x))) -
Answer:162
+
Answer:162

Problem 43

@@ -183,7 +183,7 @@

Problem 43

print(sum(numbers)) -
Answer:16695334890
+
Answer:16695334890
There are 6 such numbers: 1460357289, 1430952867, 1406357289, 4160357289, 4130952867, 4106357289
@@ -385,7 +385,7 @@

Problem 44

i += 1 -
Answer:5482660
+
Answer:5482660
\(P_{1912}=P_{2167}-P_{1020}\) and \(P_{2395}=P_{2167}+P_{1020}\)
The next 3 solutions (k,j,i) are (121168,111972,46303), (110461,95506,55500), (91650,52430,75172)
@@ -549,7 +549,7 @@

Problem 45

  • \(T_{2084377905}=P_{1203416145}=H_{1042188953}=2172315626468283465\)
    • -
    Answer:1533776805
    +
    Answer:1533776805
    \(T_{55385}=P_{31977}=H_{27693}\)

    Problem 46

    @@ -590,7 +590,7 @@

    Problem 46

    n += 2 -
    Answer:5777
    +
    Answer:5777
    There is only 1 other known counterexample: 5993

    Problem 47

    @@ -653,7 +653,7 @@

    Problem 47

    sieve_size *= 2 # double sieve size to try again -
    Answer:134043
    +
    Answer:134043
    \(134043=3\cdot7\cdot13\cdot491\)
    \(134044=2^2\cdot23\cdot31\cdot47\)
    \(134045=5\cdot17\cdot19\cdot83\)
    @@ -711,7 +711,7 @@

    Problem 48

    print(sum(modexp(x,x,10**10) for x in range(1,1+1000)) % 10**10) -
    Answer:9110846700
    +
    Answer:9110846700

    Problem 49

    @@ -776,7 +776,7 @@

    Problem 49

    print(''.join(map(str,sol))) -
    Answer:296962999629
    +
    Answer:296962999629
    (2969, 6299, 9629), step size is also 3330

    Problem 50

    @@ -831,7 +831,7 @@

    Problem 50

    print(lsum) -
    Answer:997651
    +
    Answer:997651
    diff --git a/mathstyles.css b/mathstyles.css index 11ed7fb..703088d 100644 --- a/mathstyles.css +++ b/mathstyles.css @@ -19,21 +19,23 @@ body { box-sizing: border-box; } -table { +.table_normal { border-collapse: collapse; margin: 0 auto; } -th { +.table_normal th { background: lightgray; + border: 1px solid black; + padding: 2px; } -th, td { +.table_normal td { border: 1px solid black; padding: 2px; } -details { +.pe_answer { background: lightgray; }
    number range total digits