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Given:

A, B, C are 3 distinct primes.

Find the smallest composite number Y that satisfies the relation:

$ Y = A ^ C + B ^ B + C ^ A $

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The goal is to minimize, so you'll need to obviously use the primes

$2, 3, 5$

Then

The $5$ can't be in the middle as $5^5$ is large, so it must be on either side. $(2^5 + 3^3) < (3^5 + 2^2)$, so your equation is $2^5 + 3^3 + 5^2$.

This means

$(A, B, C) = (2, 3, 5)$ and $Y = 84$

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I totally agree with the answer given by @Aranlyde.

But you don't explicitly specify that $A\not=B\not=C$.
So, I would do something like $A=B=C=2$.
Then, the result would be:

$Y=A^C+B^B+C^A=2^2+2^2+2^2=4+4+4=12$

In any way, this is the minimum.

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  • $\begingroup$ Three prime pals refer to three different..i will edit to add distinct..thx $\endgroup$ – Uvc May 16 at 18:22
  • $\begingroup$ Okay, well. Then my answer is incorrect, of course. :) $\endgroup$ – Ardoris May 16 at 18:32

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