Question

Find all primes \(p\) such that \(41p+1\) is a perfect square

Answer 1

so... 41 is prime ya?

Answer 2

i bet it is too easy for you to see that lol

Answer 3

haha yea, but so isn't this like an extension of mersenne numbers?

Answer 4

i think this problem is easier than it appears :)

Answer 5

oh wait, this is a special number theory prperty isn't it? like \(2^p+1\equiv 0 mod p\)

Answer 6

we can do it using simple algebra i guess... double click below for a spoiler :P
\(
\color{white}{41p+1 = n^2 \implies 41p = n^2-1 = (n-1)(n+1)}
\)

Answer 7

double click?

Answer 8

oh you \(\color\white{SUCK}\).

Answer 9

maybe select the bottom line instead of double clicking..

Answer 10

wouldn't that be an equation with 2 unknowns

Answer 11

and I got it, try doing it to my "oh you ." post above

Answer 12

yeah i know i suck

Answer 13

:P

Answer 14

your first reply might help :
`so... 41 is prime ya?`

Answer 15

I have noo clue... but I need to finish this graph theory homework due in like 8 hours, so I'll look at this some other time

Answer 16

One might be tempted to say 39 and 43... =)

Answer 17

39 aint no prime

Answer 18

It's a hint haha.

Answer 19

oo