Euler 120 - Square remainders.ipynb

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    "# Euler Problem 120\n",
    "\n",
    "Let $r$ be the remainder when $(a−1)^n + (a+1)^n$ is divided by $a^2$.\n",
    "\n",
    "For example, if $a = 7$ and $n = 3$, then $r = 42$: \n",
    "$6^3 + 8^3 = 728 \\equiv 42 \\pmod{49}$.\n",
    "\n",
    "And as $n$ varies, so too will $r$, but for $a = 7$ it turns out that $r_{max} = 42$.\n",
    "\n",
    "For $3 \\le a \\le 1000$, find $\\sum r_{max}$."
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      "333082500\n"
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   "source": [
    "def rmax(a):\n",
    "    t1 = t2 = 1\n",
    "    aa = a*a\n",
    "    Table = {(1,1):1}\n",
    "    rm = 2 % aa\n",
    "    while 1:\n",
    "        t1 = ((a-1)*t1) % aa\n",
    "        t2 = ((a+1)*t2) % aa\n",
    "        rm = max(rm, (t1+t2)%aa)\n",
    "        if (t1, t2) in Table:\n",
    "            return rm\n",
    "        Table[(t1,t2)] = 1\n",
    "\n",
    "print(sum(rmax(a) for a in range(3,1001)))"
   ]
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