MathDB

A 19

Source:

May 25, 2007

inductionmodular arithmeticLaTeXDivisibility Theorynumber theory

Problem Statement

Let

f(x)=x^3 +17

. Prove that for each natural number

n \ge 2

, there is a natural number

x

for which

f(x)

is divisible by

3^n

but not

3^{n+1}