id	title	challengeType	forumTopicId	dashedName
5900f3e71000cf542c50fefa	Problem 123: Prime square remainders	5	301750	problem-123-prime-square-remainders

--description--

Let p_n be the n$th prime: 2, 3, 5, 7, 11, ..., and let $r be the remainder when {(p_n−1)}^n + {(p_n+1)}^n is divided by {p_n}^2.

For example, when n = 3, p_3 = 5, and 4^3 + 6^3 = 280 ≡ 5\\ mod\\ 25.

The least value of n for which the remainder first exceeds 10^9 is 7037.

Find the least value of n for which the remainder first exceeds 10^{10}.

--hints--

primeSquareRemainders() should return 21035.

assert.strictEqual(primeSquareRemainders(), 21035);

function primeSquareRemainders() {

  return true;
}

primeSquareRemainders();

// solution required