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MathNet 2026 — Part 03 Question 161

Math Olympiad Vault · MathNet 2026 — Part 03

Question 161

The natural numbers $22$, $23$, and $24$ have the following property: The exponents of the prime factors of their decomposition are all odd: $$
22=2^{1} \cdot 11^{1} ; \quad 23=23^{1} ; \quad 24=2^{3} \cdot 3^{1}
$$ What is the largest number of consecutive natives that this property can have? reason is the answer.