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Board 8 > An easy and a brutally difficult triple prime number problem.

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FLOUR
04/27/24 4:04:43 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?

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azuarc
04/27/24 4:10:12 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.)

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Paratroopa1
04/27/24 4:11:14 PM
#3:


I dunno, probably like, 4
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azuarc
04/27/24 4:23:50 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

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azuarc
04/27/24 4:27:33 PM
#5:


oh, I think the second half of that is wrong. I set it equal to zero. That doesn't quite work.

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FFDragon
04/27/24 4:31:54 PM
#6:


My birthday is 1013 let's go with that

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jcgamer107
04/27/24 8:18:15 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

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Reg
04/27/24 8:25:48 PM
#8:


This feels distinctly like we're being asked to do somebody's homework for them.
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