PUMaC 2014 · 加试 · 第 2 题

PUMaC 2014 — Power Round — Problem 2

(15) Given the following information: 2 2 2 m (a) x + y + 2 z represents all integers not of the form 4 (16 n + 14) 2 2 2 m (b) x + y + 3 z represents all integers not of the form 9 (9 n + 6) 2 2 2 m (c) x + 2 y + 2 z represents all integers not of the form 4 (8 n + 7) 2 2 2 m (d) x + 2 y + 3 z represents all integers not of the form 4 (16 n + 10) 2 2 2 m (e) x + 2 y + 4 z represents all integers not of the form 4 (16 n + 14) 2 2 2 m (f) x + 2 y + 5 z represents all integers not of the form 25 (25 n + 10) m or 25 (25 n + 15) 2 2 2 2 classify all universal conic polynomials of the form ax + by + cz + dw . 7 Bonus Problems This section asks problems that diverge from previous problems and look at more general polynomials. Hence they are, in some sense, irrelevant to the theory - hence the name. These are interesting problems that deserve attention tho!

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