# 2023 and Sums of Squares

## Number puzzles to welcome the new year!

Some numbers can be expressed as the sum of squares of two positive integers, while others cannot. The number 2020 can, for example, because 2020 = 16² + 42².

## Problem 1

Can 2023 be expressed as the sum of squares of two positive integers?

## Problem 2

Can 2²⁰²³ be expressed as the sum of squares of two positive integers?