I have tried a number of methods using prime factorisations but they inevitably lead to invoking too many unknowns for me and balloon in complexity.
Prove there are infinitely many integer solutions to $z^z = y^y x^x$ for with $x,y,z > 1$
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number-theory
prime-numbers
prime-factorization
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0do u have any example for such numbers? – 2017-01-26
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0I do have some, and they were quite a challenge to find. – 2017-01-26
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1can u post any such numbers, just for curiosity, – 2017-01-26
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1This is an old problem of Erd\H{o}s, referenced in Guy's Unsolved Problems in Number Theory (D13). Chao Ko found infinitely many solutions, the smallest of which has $x=12^6$, $y = 6^8$ and $z=2^{11} 3^7$. – 2017-01-28