add a few more thoughts

notebooks/problem0066.ipynb

@@ -51,11 +51,9 @@
    "outputs": [],
    "source": [
     "def minimal_solution(d):\n",
-    "    var('x,y')\n",
-    "    \n",
     "    sols = solve_diophantine(x^2 - d*y^2 == 1)\n",
     "    u, v = sols[0]\n",
-    "    return (abs(u(t=0).simplify_full()), abs(v(t=0).simplify_full()))"
+    "    return (abs(u(t=0)), abs(v(t=0)))"
    ]
   },
   {
@@ -145,6 +143,35 @@
     "max((d for d in range(1, 1001) if not is_square(d)), key=lambda x: pell_fundamental_solution(x)[0])"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "3f573e65",
+   "metadata": {},
+   "source": [
+    "And in case you want to know the minimal $x$ for $x^2 - 661y^2 = 1$:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "b4b119a0",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(16421658242965910275055840472270471049, 638728478116949861246791167518480580)"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pell_fundamental_solution(661)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "cfb42d20",