use lagrange's theorem to show that if p is a prime and f(x) is a polynomial of degree n with integer coefficients and more than n roots modulo p, then p divides every coefficient of f(x)

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- Jul 7th 2009, 12:05 PMsilentbobprimitive roots
use lagrange's theorem to show that if p is a prime and f(x) is a polynomial of degree n with integer coefficients and more than n roots modulo p, then p divides every coefficient of f(x)

- Jul 7th 2009, 12:49 PMBruno J.
Hint : show that the constant term is divisible by $\displaystyle p$ by considering $\displaystyle f(0)$.

Next consider $\displaystyle (f(x)-f(0))/x$ and keep doing the same thing.