Crazy

Number Theory Level 3

Find the smallest positive integer $k$ such that $2^{69} + k$ is divisible by 127.

1 solution

Dev Sharma
Oct 13, 2015

$2^7 = 1(mod127)$ implies that

$2^{7m} = 1 (mod127)$ hence

$2^{69} = 64 (mod127)$

so minimum of k is 127 - 64 = 63