Ellie-We had that in our math class as well...thank you very much!
lol! More like your trying to get the ansewer for this weeks Lenny Conundrem on neopets.com!
I'm much rather have the extra 10 points on the exam, then try and win pretty much nothing on neopets.com. Can't help it if my math teacher used that question as well.
Anywho...just so the admin who helped with the question knows..the answer is 0.
"what is the number of prime numbers between one and a million that become a perfect square if you add 1 to them?"
Surely the number 3 qualifies ... add 1 you get 4 which is 2*2
So the answer is 1, isn't it?
just came here while googling...
so, a formal proof:
p be such a prime number,
=> p+1 = n^2, where n is natural =>
=> p = n^2 - 1
=> p = (n-1)(n+1), but hey, p is prime!
=> that can only be if n-1 = 1, that is p = 3
=> only one such prime number
Way cool, jaz. Neat and simple.
Ummm ... don't just drop a pearl of wisdom in passing ... join up and give us a few (not TOO hard) puzzles, or help out at the "Help Me" forum. (Though things may be quietening down here soon, as Summer Holidays are nearly upon us!)