Problem

TxO Math Bowl 2024 - Team Contest - Problem 19

Two quadratics p(x) and q(x) have all of their coefficients selected from the set \{1, 2, 3, \dots, 10\} such that p(a) \equiv q(a) \pmod 3 for all integers a. Given that p(x) - q(x) has exactly one real root, how many pairs (p(x), q(x)) exist?


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Problem Tags: Algebra Counting and probability Number theory

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