How to solve $a^bc^d = abcd$ where $ a, b, c,d \in $Z

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Is there a solution to this? notes that a, b, c, d are different integers.

I have tried to solve it with algebra and my equations are leading me in circles.

I know that 0 and 1 solve this. Are there other integers?

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1 Answer

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Think of a prime $p$ that divides $a$. How many factors of $p$ are on each side?

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