diff --git a/doc/kryptools.ipynb b/doc/kryptools.ipynb
index e72b22a..d9285c9 100644
--- a/doc/kryptools.ipynb
+++ b/doc/kryptools.ipynb
@@ -53,7 +53,7 @@
     {
      "data": {
       "text/plain": [
-       "3 (mod 5)"
+       "3"
       ]
      },
      "execution_count": 2,
@@ -82,7 +82,7 @@
     {
      "data": {
       "text/plain": [
-       "0 (mod 5)"
+       "0"
       ]
      },
      "execution_count": 3,
@@ -103,7 +103,7 @@
     {
      "data": {
       "text/plain": [
-       "2 (mod 5)"
+       "2"
       ]
      },
      "execution_count": 4,
@@ -429,7 +429,7 @@
    "id": "bea6a5f6-911f-4154-95c1-8e841d8a0930",
    "metadata": {},
    "source": [
-    "Since it equals $+1$ the number has a [quadratic residue](https://en.wikipedia.org/wiki/Quadratic_residue) and has a square root modulo the prime $7$"
+    "Since it equals $+1$ the number is a [quadratic residue](https://en.wikipedia.org/wiki/Quadratic_residue) and has a square root modulo the prime $7$"
    ]
   },
   {
@@ -591,7 +591,7 @@
     {
      "data": {
       "text/plain": [
-       "[57, 1579]"
+       "[3, 19, 1579]"
       ]
      },
      "execution_count": 18,
@@ -610,7 +610,7 @@
    "id": "450c25e8-1654-4177-9de3-1c4f8d41024a",
    "metadata": {},
    "source": [
-    "Pollard $p-1$ (in this case no factor is found)"
+    "Pollard $p-1$"
    ]
   },
   {
@@ -641,7 +641,7 @@
    "id": "3d847314-d9af-4a72-af15-374755d6ff93",
    "metadata": {},
    "source": [
-    "Lentstra's ECM"
+    "Lentstra's ECM  (if no factor is found, `None` is returned)"
    ]
   },
   {
@@ -1929,7 +1929,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.1"
+   "version": "3.12.2"
   }
  },
  "nbformat": 4,