Nice and hard problem!
Posted: Sun May 07, 2017 6:36 pm
Let $f(n)$ polynomial (not costant) with integer coefficients and:
If n is an odd number $2f(n)^{4}=f(f(n)^{2}-458)+1832f(n)^{2}$
If m is an even number
$f(m)-f(1)$ is multiple of $m+1$.
Find $f(457)+f(459)+f(461)$
If n is an odd number $2f(n)^{4}=f(f(n)^{2}-458)+1832f(n)^{2}$
If m is an even number
$f(m)-f(1)$ is multiple of $m+1$.
Find $f(457)+f(459)+f(461)$