Unformatted text preview: (d) The binomial theorem shows that this polynomial is of the form x p1 + 2 px p2 + ··· + 2 p1 p . The coefﬁcients of x i for 0 ≤ i ≤ p2 are all divisible by p ; it is crucial that p is prime here. Also p 2 does not divide 2 p1 p (here it is crucial that p 6 = 2). Now apply Eisenstein for the prime p (of course, it is crucial that p is prime here)....
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 Fall '07
 PALinnell
 Algebra, Polynomials, Prime number, Eisenstein, Apply Eisenstein

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