Moody Modulus

Number Theory Level 2

Let $f(n)$ be the remainder when $6$ is divided by $n$ . Find $f(1)+f(2)+f(3)+\ldots+f(89)+f(90)$ .

507 505 506 504

1 solution

Lu Chee Ket
Jan 29, 2015

6 MOD 1 = 6 MOD 2 = 6 MOD 3 = 6 MOD 6 = 0,

6 MOD 4 = 2,

6 MOD 5 = 1

The rest are all 6 which is (90 - 7 + 1) x 6 i.e. 504

0 + 0 + 0 + 2 + 1 + 0 + 504 = 507