MathDB

2n^2+2n+1 is composite

Source: Romanian 2018 TST Problem 2 Day 2

May 25, 2020

number theoryquadratic reciprocitySum of Squarescomposite numbers

Problem Statement

Show that a number

n(n+1)

where

n

is positive integer is the sum of 2 numbers

k(k+1)

and

m(m+1)

where

m

and

k

are positive integers if and only if the number

2n^2+2n+1

is composite.