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Easy problem
Posted:
Wed Apr 11, 2007 10:03 pmby 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...
Re: Easy problem
Posted:
Wed Apr 11, 2007 10:57 pmby makashi
Posted:
Thu Apr 12, 2007 5:41 pmby zefuri
whats the sophie germain identity
Posted:
Thu Apr 12, 2007 6:02 pmby 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
Posted:
Thu Apr 12, 2007 6:05 pmby 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?
Posted:
Thu Apr 26, 2007 10:00 pmby 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.
Posted:
Thu Apr 26, 2007 11:25 pmby kashhustler
Posted:
Thu Apr 26, 2007 11:34 pmby 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.
Posted:
Fri Apr 27, 2007 10:46 amby zefuri
so basically up until that part you go (see Makashi's proof)