# Thread: Equation with primes in exponent

1. ## Re: Equation with primes in exponent

Originally Posted by godelproof
I agree~

BTW, Do you believe $\displaystyle {2}^{p}+{3}^{p}={a}^{n}\Longrightarrow n=1$, for ANY positive integer p? See here http://www.mathhelpforum.com/math-he...ed-183583.html
i will work on it. nice problem.

2. ## Re: Equation with primes in exponent

Originally Posted by tonio
Now you've finally produced something that looks like a proof (though I still shall check about the distributivity of that LT function, which right now I've not

time to do and isn't clear to me at once).

This is all I was asking before.

Tonio
His $\displaystyle \text{LT}(x) = x \mod 100$, so there is no need to verify distributivity.

The LT() proof and the congruence proofs are actually the same.

$\displaystyle x \mod 100$ can be split into two congruences, namely $\displaystyle x \mod 25$ and $\displaystyle x \mod 4$ since they are relatively prime

Abhishek's proof realizes that we can just focus on $\displaystyle x \mod 25$ part

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