Clan x86

General Forums => Academic / School => Math and Other Problems => Topic started by: Ender on July 26, 2007, 01:51:11 am

Title: Perfect Squares Problem #2
Post by: Ender on July 26, 2007, 01:51:11 am

Find, with proof, all positive integer values n such that (http://latex.sidoh.org/?render=-5%5E4%20%2B%205%5E5%20%2B%205%5En%20) is a perfect square.

EDIT: Added in the "with proof" clause because that's really in the spirit of the question.

Title: Re: Perfect Squares Problem #2
Post by: rabbit on July 26, 2007, 10:34:11 am

-(5^4) or (-5)^4?

Title: Re: Perfect Squares Problem #2
Post by: Ender on July 26, 2007, 11:03:31 am

-(5^4)

Title: Re: Perfect Squares Problem #2
Post by: rabbit on July 26, 2007, 02:24:04 pm

n = 5 yielding 2500+5^n = 5625, which is 75^2.  There are others, I'm sure, but eh?

Title: Re: Perfect Squares Problem #2
Post by: Ender on July 27, 2007, 12:32:14 am

Yep, n = 5 is one of the solutions. What are the others? Are there any others? And prove it :P