Problem 2. Verify that $1009=15^{2}+28^{2}$, and represent the number 2018 as the sum of two squares of natural numbers.
Answer: $2018^{2}=13^{2}+43^{2}$.

Solution. The given equality can be verified directly. Let $a=15, b=28$. Then $1009=a^{2}+b^{2}, 2018=2 a^{2}+2 b^{2}=(a+b)^{2}+(a-b)^{2}=13^{2}+43^{2}$.

Answer to variant 2: $3866^{2}=29^{2}+55^{2}$.