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COMMENTS
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Solutions z of the Diophantine equation x^y * y^x = (x+y)^z with 1 <= x <= y. This Diophantine equation was problem 2 of Day 1 for the 2015 Kazakhstan National Olympiad, see Art of Problem Solving and Diophante links. Some results:
-> x and y are both even.
-> This equation has solution iff x = y.
-> The equation becomes x^(2x) = (2x)^z.
-> Corresponding triples (x,y,z) that are solutions satisfy:
x = y = 2^(2^n-1) = A058891(n+1) for n >= 1, and,
z = a(n) = (2^n-1) * 2^(2^n-n) for n >= 1.
-> First triples solutions are (x,y,z) = (2,2,2), (8,8,12), (128,128,224), (32768,32768,61440), ...
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