14.22. How many pairs of integers $x, y$, lying between 1 and 1000, are there such that $x^{2}+y^{2}$ is divisible by $7 ?$
14.22. Answer: $142^{2}=20164$. The number $x^{2}+y^{2}$ is divisible by 7 if and only if both numbers $x$ and $y$ are divisible by 7. Indeed, the square of an integer when divided by 7 gives remainders of $0,1,2$, and 4. The number of integers between 1 and 1000 that are divisible by 7 is 142. Therefore, the desired number is $142^{2}=20164$.