PUMaC 2025 · 数论（A 组） · 第 3 题

PUMaC 2025 — Number Theory (Division A) — Problem 3

Compute the sum of all primes p < 50 such that there exist linear multinomials P and Q with 2 2 integer coefficients such that x − 2 xy − y ≡ P ( x, y ) · Q ( x, y ) (mod p ). A linear multinomial is an expression of the form ax + by + c . k ( p ) k 2

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