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Square Sum and Square Multiple (Posted on 2015-09-13) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Solution 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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