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Part of 1999 Greece JBMO TST

Problems(1)

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

Source: Greece JBMO TST 1999

5/25/2019
Examine whether exists n∈N∗n \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
number theoryperfect cubePerfect PowersPerfect power