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integer polynomial p(x) with p(7) = 77, p(m) = 0, and p(n) = 85

Source: Israel Joseph Gillis Mathematical Olympiad 1998 p6

February 16, 2020

polynomialInteger Polynomial

Problem Statement

Find all pairs

(m,n)

of integers with

m > n > 7

for which there exists a polynomial

p(x)

with integer coefficients such that

p(7) = 77, p(m) = 0

, and

p(n) = 85