What are nasty numbers?

Nasty numbers are integers that cannot be expressed as the sum of two non-negative perfect squares. In other Words, a nasty number cannot be represented in the form ( a^2 + b^2 ) where ( a ) and ( b ) are non-negative integers. Examples of nasty numbers include values like 3, 7, and 11. This concept is often explored in number theory and relates to the properties of quadratic residues.