Proof writing for polynomials – math.stackexchange.com

Let the polynomial $f(x)=x^n+a_1 x^{n-1}+a_2 x^{n-2}+.....a_{n-1}x+a_n$ have integral coefficients. If there exists four distinct integers $a,b,c$ and $d$ such that $f(a)=f(b)=f(c)=f(d)=5$ show that ...

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