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Polynomial # 1 (Posted on 2006-05-26) Difficulty: 3 of 5
Let f(x) be a nonconstant polynomial in x with integer coefficients and suppose that for five distinct integers a1, a2, a3, a4, a5, one has f(a1)= f(a2)= f(a3)= f(a4)= f(a5)= 2.

Find all integers b such that f(b)= 9.

No Solution Yet Submitted by Ravi Raja    
Rating: 5.0000 (1 votes)

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re: Solution (spoiler) | Comment 5 of 7 |
(In reply to Solution (spoiler) by e.g.)

That h(x) is a polynomial with integer coefficients is not exactly obvious.  This is a consequence of Gauss's Lemma: A polynomial with integer coefficients that cannot be factored into irreducible factors with integer coefficients also cannot be factored into irreducible factors with rational coefficients.
  Posted by Richard on 2006-05-26 23:12:04

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