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Combination of integer polynomials

Source: Romanian IMO Team Selection Test TST 1988, problem 10

October 1, 2005
algebrapolynomialalgebra proposed

Problem Statement

Let p>2 p > 2 be a prime number. Find the least positive number a a which can be represented as a \equal{} (X \minus{} 1)f(X) \plus{} (X^{p \minus{} 1} \plus{} X^{p \minus{} 2} \plus{} \cdots \plus{} X \plus{} 1)g(X), where f(X) f(X) and g(X) g(X) are integer polynomials. Mircea Becheanu.
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