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no of integers a with 1 \le a \le 100 such that a^a is a perfect square

Source: Dutch MO 2007 p4

September 1, 2019
Perfect Squarenumber theoryexponential

Problem Statement

Determine the number of integers aa satisfying 1≤a≤1001 \le a \le 100 such that aaa^a is a perfect square. (And prove that your answer is correct.)
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