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Prove that a=x and b=x^x - [Iran Third Round 1998]

Source: Iran Third Round MO 1997, Exam 3, P1

October 18, 2005
number theory proposednumber theory

Problem Statement

Suppose that a,b,xa, b, x are positive integers such that xa+b=abbx^{a+b}=a^bb Prove that a=xa=x and b=xxb=x^x.
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