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## Homework Statement

Let m be the number of numbers fromantic the set {1,2,3,...,2014} which can be expressed as difference of squares of two non negative integers. The sum of the digits of m is ...

## Homework Equations

## The Attempt at a Solution

I got a solution from a magazine but I didn't under stand how it came

Can anyone explain me how it came.

Answer is as follows:

2n+1=(n+1)^2 -n^2

n^3=[n (n+1)/2]^2 - [n (n-1)/2]^2

Therefore m contains all odd numbers and the even numbers 2^3,4^3,8^3,10^3,12^3.

Therefore m=1007+7=1013 with digit sum 5.