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MathNet 2025 — Part 01 (100 complete bilingual questions) Question 31

Math Olympiad Vault · MathNet 2025 — Part 01 (100 complete bilingual questions)

Question 31

We will call *smalls* the positive integers not larger than $2025$.

a) Find the number of smalls which are perfect squares.

b) Find the number of smalls which are perfect squares and leave remainder $0$ when divided by $45$.

c) Find the number of smalls which neither are perfect squares, nor leave remainder $0$ when divided by $45$.