perplexus.info :: Just Math : Four special natural numbers

Four special natural numbers (Posted on 2008-12-11)

Find all sets of four natural numbers such that the square of each of them, when added to the sum of the other three, again yields a perfect square.

Submitted by pcbouhid

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Solution: (Hide)

Let the numbers be m, n, p and q. The sets are:

m = n = 96, p = 57, q = 10

m = n = 11, p = q = 6

m = n = p = k*(3k +- 2), q = 1

m = n = p = q = 1.

There´s no set with all different m, n, p, q.

Those who might be interested in the whole analytical solution (it´s a little extense), write me.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Is there a pattern to this?	Charlie	2008-12-12 11:18:18
Is there a pattern to this?	brianjn	2008-12-12 04:43:00
computer exploration--is there a pattern to this?	Charlie	2008-12-12 00:17:29
re: a start	Dej Mar	2008-12-11 22:48:58
re(2): No Subject	brianjn	2008-12-11 22:40:03
a start	xdog	2008-12-11 22:16:25
re: No Subject	JayDeeKay	2008-12-11 20:59:08
No Subject	brianjn	2008-12-11 20:14:02

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