An easy and a brutally difficult triple prime number problem.

Board 8

Board 8 » An easy and a brutally difficult triple prime number problem.
FLOUR
04/27/2024
04:04 PM
#1
Suppose p,q,r are all primes such that p>q>r and p-q=r . What is the value of r? Yup, that's the easy one.

Now for the sinister problem:

Suppose p,q,r are all distinct primes less than 2027 and p^r - q^r is divisible by 2027. What is the value of r?
You wish to fill Lionel's coffers? Yes, ha, ha, ha, yes!!!
azuarc
04/27/2024
04:10 PM
#2
5-3=2

Let's just get that out there. Primes are all odd beside 2, so they must be an even amount apart. (Could also be other pairs like 5 and 7, or 71 and 73, but r must be 2.)
Only the exceptions can be exceptional.
Paratroopa1
04/27/2024
04:11 PM
#3
I dunno, probably like, 4
azuarc
04/27/2024
04:23 PM
#4
I can prove r is not 2 or 3 using modulo and difference of squares/cubes. Those have solutions, but they don't satisfy p>q>r because q has to be 2. I'm not sure of a method for exploring r = 5, 7, 11, etc.

https://gamefaqs.gamespot.com/a/forum/c/cc5f0528.jpg
Only the exceptions can be exceptional.
azuarc
04/27/2024
04:27 PM
#5
oh, I think the second half of that is wrong. I set it equal to zero. That doesn't quite work.
Only the exceptions can be exceptional.
FFDragon
04/27/2024
04:31 PM
#6
My birthday is 1013 let's go with that
If you wake up at a different time, in a different place, could you wake up as a different person?
#theresafreakingghostafterus
jcgamer107
04/27/2024
08:18 PM
#7
FLOUR posted...
Suppose p,q,r are all primes such that p>q>r and p-q=r . What is the value of r?
azuarc posted...
5-3=2
Yeah - that's easy, it's-

FLOUR posted...
Suppose p,q,r are all distinct primes less than 2027 and p^r - q^r is divisible by 2027. What is the value of r?
Bye
azuarc wasn't even home. he was playing Magic the Gathering at his buddy's store, which is extremely easy to verify
Reg
04/27/2024
08:25 PM
#8
This feels distinctly like we're being asked to do somebody's homework for them.
Board 8 » An easy and a brutally difficult triple prime number problem.