perplexus.info :: Just Math : Square Sum and Square Multiple

Square Sum and Square Multiple (Posted on 2015-09-13)

Find the four smallest positive integer solutions to this equation:

X² + Y² = 2017*Z²

Note: “Four smallest solutions” mean the solutions with the four smallest values of X+Y.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

Based on Steve Herman's Solution:
When z = 1, the only solutions are (9,44) and (44,9) When z = 2, the only solutions are (18,88) and (88,18) When z = 3, the only solutions are (27,132) and (132,27) When z = 4, the only solutions are (36,176) and (176,36) When z = 5, the solutions are (45,220),(96,203),(149,168), and their "reverses". So, the 4 smallest solutions are (9,44), (44,9), (18,88) and (88,18). The 4 smallest distinct values of X + Y are 53, 106, 153, and 212.

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

Subject	Author	Date
An extended list -- Using Visual Basic	Charlie	2015-09-13 14:54:43
Using Excel (spoiler)	Steve Herman	2015-09-13 08:53:43

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