6.1. How many numbers from 1 to 1000 (inclusive) cannot be represented as the difference of two squares of integers
Answer: 250.

Solution. Note that any odd number $2n+1$ can be represented as $(n+1)^{2}-n^{2}$. Moreover, an even number that is a multiple of 4 can be represented as $4n=(n+1)^{2}-(n-1)^{2}$. The numbers of the form $4n+2$ remain. Note that a square can give remainders of 0 or 1 when divided by 4, so numbers of the form $4n+2$ cannot be obtained as the difference of squares. There is exactly one such number (of the form $4n+2$) in every set of four consecutive numbers, so the total number of such numbers from 1 to 1000 will be $1000 / 4 = 250$.