[seqfan] n = x*y*z , x + y - z = 1
Georgi Guninski
guninski at guninski.com
Sat Oct 23 12:56:18 CEST 2010
n = x*y*z
x + y - z = 1
all positive integers
can one maximize the number of solutions ?
every solution is integral point on genus 1:
x*y*(x+y-1) = n
brute force approach doesn't seem promising, partially because for large number of divisors counting the solutions is not fast.
solutions n include all squares and start:
4, 9, 16, 24, 25, 36, 40, 49, 60, 64, 72, 81, 84, 100, 105, 112, 121,
144, 160, 169, 180, 189, 196, 216, 220, 225, 240, 256, 264, 280, 289,
297, 300, 312, 324, 352, 360, 361, 364, 385, 400, 420, 429, 432, 441,
480, 484, 504, 520, 529, 544, 576, 585, 612, 616, 624, 625, 672, 676,
684, 700, 720, 729, 756, 760, 765, 784, 825, 832, 840, 841, 864, 900,
924, 945, 952, 960, 961, 969
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