PUMaC 2008 · 代数（B 组） · 第 9 题

PUMaC 2008 — Algebra (Division B) — Problem 9

(7 points) Find the polynomial f with the following properties: • its leading coefficient is 1, • its coefficients are nonnegative integers, • 72 | f ( x ) if x is an integer, • if g is another polynomial with the same properties, then g − f has a nonnegative leading coefficient. ( ) p ( x ) 1

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