The Beginning

Algebra Level 3

Find the remainder when $x^{2555} + 2555$ is divided by $x+1$

This problem is a part of this set .

3 solutions

Rhoy Omega
Aug 10, 2014

Define $f(x)$ = $x^{2555} + 2555$ .

Then by the Remainder-Factor Theorem, $f(x)$ divided by $x + 1$ is just $f(-1)$ , since $x + 1 = x - (-1)$ .

This gives us $f(-1) = (-1)^{2555} + 2555 = \boxed{2554}$

Fox To-ong
Jan 14, 2015

just substitute x = -1

Kenny Lau
Sep 9, 2014

Note that $x+1|x^{2n+1}+1$ .

$x^{2555}+2555$ $=x^{2555}+1+2554$ $\equiv2554$

(That is when x>2554)