The title really says it all. My research adviser showed me the problem: is not prime, apparently. He said that the proof is very short, elegant and elementary, but that he couldn't have seen it unless someone showed him. I also don't see it.

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- Jun 1st 2012, 10:22 PMskeptopotamus2^46 + 5^40 Not Prime - How to Prove?
The title really says it all. My research adviser showed me the problem: is not prime, apparently. He said that the proof is very short, elegant and elementary, but that he couldn't have seen it unless someone showed him. I also don't see it.

- Jun 2nd 2012, 03:18 AMBobPRe: 2^46 + 5^40 Not Prime - How to Prove?

Therefore,

and the RHS factors as the difference of two squares. - Jun 2nd 2012, 04:58 AMskeptopotamusRe: 2^46 + 5^40 Not Prime - How to Prove?
Awesome, thanks! I'm usually quite good at these types of problems, but I just didn't see this one. I went at it cohomologically after a direct check on primes up to 37 didn't work, which went nowhere.

- Jun 7th 2012, 10:34 PMSarasijRe: 2^46 + 5^40 Not Prime - How to Prove?
- Jun 8th 2012, 10:06 AMskeptopotamusRe: 2^46 + 5^40 Not Prime - How to Prove?
There is not a general way to do these types of problems, unfortunately. However, specifically can be solved using the most elementary technique of just manually checking for primes less than, say, 31 or so. That is how I start any of these problems, given that of course the vast majority of odd numbers are divisible by one of these primes.

For example:

- Jun 8th 2012, 08:55 PMSarasijRe: 2^46 + 5^40 Not Prime - How to Prove?
Got it...thanks...

- Jun 29th 2012, 10:47 PMharryphamRe: 2^46 + 5^40 Not Prime - How to Prove?
- Jun 30th 2012, 07:50 AMskeptopotamusRe: 2^46 + 5^40 Not Prime - How to Prove?