# Cathy’s Composite party is powered by three Prime Pals. Can you find them?

Given:

A, B, C are 3 distinct primes.

Find the smallest composite number Y that satisfies the relation:

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

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 $$Y = 84$$

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.

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