A, B, C are 3 distinct primes.

Find the smallest composite number Y that satisfies the relation:

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


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

$2, 3, 5$


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 $Y = 84$


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:


In any way, this is the minimum.

New contributor
Ardoris is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.