MathDB

2016 Latvia National Olympiad 3rd Round Grade12Problem4

Source:

July 22, 2016

functionalgebra

Problem Statement

Two functions are defined by equations:

f(a) = a^2 + 3a + 2

and

g(b, c) = b^2 - b + 3c^2 + 3c

. Prove that for any positive integer

a

there exist positive integers

b

and

c

such that

f(a) = g(b, c)