MathDB

every integer can be written in the form x^2 -y^2 +Ax+By where A+B= odd

Source: 1997 Swedish Mathematical Competition p3

April 2, 2021

number theoryodd

Problem Statement

Let

A

and

B

be integers with an odd sum. Show that every integer can be written in the form

x^2 -y^2 +Ax+By

, where

x,y

are integers.