Easy problem

[stupidityismygam]

I have an old/easy problem:

Find with proof all positive integer [unparseable or potentially dangerous latex formula]

such that [unparseable or potentially dangerous latex formula] is prime...

[makashi]

[zefuri]

whats the sophie germain identity

[stupidityismygam]

[unparseable or potentially dangerous latex formula]...i believe

dang it...i lose my 2...

basically it is what happens when you complete the square

[Kurt]

Close...[unparseable or potentially dangerous latex formula]

I had never heard of it either before seeing this thread, but I've already found it useful on another question posted, lol.

I tried to do this problem with quartic residues...it's easy for all cases except for [unparseable or potentially dangerous latex formula]

Does anyone know how to prove it for that case, using that approach?

[NickR]

By Fermat's Little Theorem,

[unparseable or potentially dangerous latex formula], so [unparseable or potentially dangerous latex formula]
Edit: This only works for all x's relatively prime to 5.

Therefore, [unparseable or potentially dangerous latex formula]

This means that the only prime number it can be is 5 because it will always be divisible by 5.

[kashhustler]

[NickR]

Ah, true...I did have a doubt about that when I wrote it and now you reminded me about the dividing in mods rule lol.

[zefuri]

so basically up until that part you go (see Makashi's proof)