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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Using Excel (spoiler)

| Comment 1 of 2

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

Posted by Steve Herman on 2015-09-13 08:53:43

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