06/18/2020 (2011: National Target Round, Problem 8)

Q: How many positive integers less than 2011 cannot be expressed as the difference of the squares of two positive integers?

A: 505

The set containing the difference of squares of positive integers contains all odd numbers (besides 1) and all multiples of 4 (besides 4).

There are 1006 odd numbers and 502 multiples of 4, so there are 1508 numbers that fit the qualifications listed previously, but now we have to subtract 2, so we get 1506 numbers that can be expressed as the difference of squares.

2011 - 1506 = 505 numbers.