1. ## polynomial mod. proof

Hey I have this proof which im a bit stuck on:

If a=b mod(n) then show that:

f(a) = f(b) (mod n) for any polynomial with integer coefficirnts

Im not too sure where to start, but I kind of get that making the polynomial degree to 0 first would be the starting point, then proving it for e.g degree k+1, help would be much appreciated thank you

2. Originally Posted by a1007
Hey I have this proof which im a bit stuck on:

If a=b mod(n) then show that:

f(a) = f(b) (mod n) for any polynomial with integer coefficirnts

Im not too sure where to start, but I kind of get that making the polynomial degree to 0 first would be the starting point, then proving it for e.g degree k+1, help would be much appreciated thank you
Hint 1: If $a\equiv b$ then $a^k \equiv b^k$.
Hint 2: If $a\equiv b$ and $c\equiv d$ then $a+c\equiv b+d$