private BigInteger ChooseM(Diophantine d, long N)
{
// we need m such that k | (a + bm) that minimizes (m^2 - N)
// first find possible m
// a + bm = 0 mod k
// => m = -a(b^-1) mod k
var sqrtN = (int)Math.Sqrt(N);
var k = BigInteger.Abs(d.k);
var invB = Modular.ModularMultiplicativeInverse(d.b, k); // apparently gcd(b, k) = 1 always, so this is legit ¯\_(ツ)_/¯
var m = (-d.a) * invB;
var m0 = m + ((sqrtN - m) / k) * k;
var m1 = m + ((sqrtN - m) / k + 1) * k;
return(new[] { m0, m1 }.OrderBy(x => BigInteger.Abs(x * x - N)).First());
}
