## Let p be a prime integer, and let f in Z[x] be a polynomial of degree 2n+1

Let p be a prime integer, and let f in Z[x] be a polynomial of degree 2n+1
say f(x)=a2n+1 x^2n+1 + ...+a1x + a0
suppose that an+1 does not equal 0 mod p
a0...an = 0 mod p^2
an+1...a2n=0 mod p
a0 is not equal to 0 mod p^3
prove that f is irreducible in Q[x]