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a^A = b^B = c^C = 1990^{1990}abc where A = b^c, B = c^a, C = a^b

Source: Austrian - Polish 1990 APMC

May 7, 2020
diophantineDiophantine equationnumber theory

Problem Statement

Find all solutions in positive integers to aA=bB=cC=19901990abca^A = b^B = c^C = 1990^{1990}abc, where A=bc,B=ca,C=abA = b^c, B = c^a, C = a^b.
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