Let p>2 be a prime number. Find the least positive number 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) and g(X) are integer polynomials.
Mircea Becheanu. algebrapolynomialalgebra proposed