Show that for any integer n there exists integers i, j, and k such that

n = i² + j² - 5k²

L.E. Dickson

(In reply to Solution by Gamer)

So, what you are saying is that n comes in two possible flavors -- even or odd.

If n is even, choose k such that k=(n-2)/2; choose i such that i=(n-4)/2; and choose j such that j=n-1.

If n is odd, choose k, i, and j such that k=(n-1)/2; i=(n+1)/2; and once again, j=n-1.

Good job!  When I first looked at this problem, it seemed daunting.  But your solution made it clear to me.  Thanks.

Posted by Mindy Rodriguez on 2005-11-25 13:08:32