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Min/max{a,b,c,d} if a^b divides b^c divides c^d divides d^a

Source: XIX Olimpíada Matemática Rioplatense (2010)

July 22, 2011
inequalitiesnumber theorynumber theory unsolved

Problem Statement

Suppose aa, bb, cc, and dd are distinct positive integers such that aba^b divides bcb^c, bcb^c divides cdc^d, and cdc^d divides dad^a. (a) Is it possible to determine which of the numbers aa, bb, cc, dd is the smallest? (b) Is it possible to determine which of the numbers aa, bb, cc, dd is the largest?
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