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3n is cube, 4n is perfect 4th power, 5n perfect 5th power, 6n perfect 6th power

Source: Greece JBMO TST 1999

May 25, 2019
number theoryperfect cubePerfect PowersPerfect power

Problem Statement

Examine whether exists nNn \in N^*, such that: (a) 3n3n is perfect cube, 4n4n is perfect fourth power and 5n5n perfect fifth power (b) 3n3n is perfect cube, 4n4n is perfect fourth power, 5n5n perfect fifth power and 6n6n perfect sixth power