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3

Part of 2001 ITAMO

Problems(1)

Two-variable exponential diophantine equation with 2001

Source: ItaMO 2001 Problem 3

2/17/2013
Consider the equation x2001=yx. x^{2001}=y^x .
[*] Find all pairs (x,y)(x,y) of solutions where xx is a prime number and yy is a positive integer.
[*] Find all pairs (x,y)(x,y) of solutions where xx and yy are positive integers.
(Remember that 2001=3⋅23⋅292001=3 \cdot 23 \cdot 29.)
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