MathDB

2

Part of 1989 Mexico National Olympiad

Problems(1)

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

7/27/2018
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
number theoryDivisors