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Math Help - polynomial mod. proof

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by a1007 View Post
    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
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