How many integers \(s\) are there such that \(0 \leq s \leq 99\) and there exists a positive integer \(n\) such that \(n^2 \) leaves a remainder of \(s\) when divided by 100?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 5 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!