diff --git a/notebooks/problem0066.ipynb b/notebooks/problem0066.ipynb index 7a6e5fe..2087729 100644 --- a/notebooks/problem0066.ipynb +++ b/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",