Impossible Modulo

Number Theory Level 3

What is the remainder when $\large{2018^{2018!}}$ is divided by $797086$ ?

1 solution

Michael Mendrin
May 13, 2018

Okay, this has got to be the wierdest, most unexpected answer, $666$

We make use of the property

$a^b$ mod $c = (a$ mod $c)^b$ mod $c$

so that we find the modulo for successive exponentiation, as follows

$a^{(b-1)b}$ mod $c = (a^{(b-1)}$ mod $c)^b$ mod $c$

until $b=2018$

This is best done with a short computer program