A STORAGE FOR THOUGHT

Let r be the remainder when (a−1)n + (a+1)n is divided by a2.For example, if a = 7 and n = 3, then r = 42: 63 + 83 = 728 ≡ 42 mod 49. And as n varies, so too will r, but for a = 7 it turns out that rmax = 42.For 3 ≤ a ≤ 1000, find ∑ rmax. r을 (a−1)n + (a+1)n 을 a2로 나눴을때의 나머지라 하자; 예를 들면 a = 7이고 n = 3이면, r = 42(63 + 83 = 728 ≡ 42 mod 49)이다. 그리고 n이 달라지면, r,도 달라질테지만, 어쨌건간에 a = 7이 경우는 r의 최댓값은 42이다. 3부터..

문제 The largest integer ≤ 100 that is only divisible by both the primes 2 and 3 is 96, as 96=32*3=25*3. For two distinct primes p and q let M(p,q,N) be the largest positive integer ≤N only divisible by both p and q and M(p,q,N)=0 if such a positive integer does not exist. E.g. M(2,3,100)=96. M(3,5,100)=75 and not 90 because 90 is divisible by 2 ,3 and 5. Also M(2,73,100)=0 because there does not ..