MathDB
2019 T15: Prime-Covering Polynomials

Source:

January 27, 2019
2019teamalgebrapolynomial

Problem Statement

Call a polynomial PP prime-covering if for every prime pp, there exists an integer nn for which pp divides P(n)P(n). Determine the number of ordered triples of integers (a,b,c)(a,b,c), with 1≤a<b<c≤251\leq a < b < c \leq 25, for which P(x)=(x2−a)(x2−b)(x2−c)P(x)=(x^2-a)(x^2-b)(x^2-c) is prime-covering.
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