Difference of two squares

Number Theory Level 4

How many integers between 1 and 100 can be written as the difference of two perfect squares?

For this problem, do not consider 0 as a perfect square.

1 solution

Tran Hieu
Feb 18, 2016

We have $a^2-b^2$ only have form $2k+1$ or $4k$ . They will not have the form $4k+2$ .

From 1 to 100 there are 49 numbers with the form $2k+1$ - We have to exclude number 1

From 1 to 100 there are 24 numbers with the form $4k$ - We have to exclude number 4.

Therefore we have $49+24=\boxed{73}$