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Bundeswettbewerb Mathematik 1989 Problem 2.1

Source: Bundeswettbewerb Mathematik 1989 Round 2

September 23, 2022

algebrapolynomialnumber theoryDivisibilitydegree

Problem Statement

Determine the polynomial

f(x) = x^k + a_{k-1} x^{k-1}+\cdots +a_1 x +a_0

of smallest degree such that

a_i \in \{-1,0,1\}

for

0\leq i \leq k-1

and

f(n)

is divisible by

30

for all positive integers

n

.

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