Re: Powers of 2


"Bob" <me13013@xxxxxxxxxxx> wrote in message
news:1142260177.933653.170930@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
I wrote:
ObPuzzle: 3 is prime and one less than a perfect square. What is the
next number with both those properties?

and Eric Sosman replied
A confirmation of Runyn's point: It took me only a couple
of minutes to write a computer program to search for the answer
(which I'll post as soon as the program finishes).

(Assuming you're not being sarcastic).

The answer is found much quicker without the aid of a program. Let me
know when your program finishes.

Bob H


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Let p be a prime which is one less than a square number.
p = n^2 - 1 for some positive integer n.
p = (n+1)(n-1)

Since p is prime, it must be the case that n-1=1, otherwise, both n-1 and
n+1 would be factors of p that were greater than or equal to 2.

Thus n = 2, and p = 3 is the only such prime with this property.

Dave


.

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