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a|b^2, b^2|a^3, a^3|b^4, b^4|a^5$, but a^5 does not divide b^6

Source: Mexican Mathematical Olympiad 1989 OMM P2

July 27, 2018
number theoryDivisors

Problem Statement

Find two positive integers a,ba,b such that a∣b2,b2∣a3,a3∣b4,b4∣a5a | b^2, b^2 | a^3, a^3 | b^4, b^4 | a^5, but a5a^5 does not divide b6b^6
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