x=1/92,y=-1/197,z=-1/205のとき、
|x+y+z|=0.0009153743……
x=25k+6 , y=-20k-8 , z=8k+5
x+y+z = 13k+3
(x,y,z) = (6,-8,5)
|x+y+z| = 3
x,y,zが整数という縛りで
(x,y,z) = (2,-54,53) で |x+y+z|=1
x=-9,y=127,z=-118で|x+y+z|=0
|x+y+z|の最小値は0
x = -9 y = 127 z = -118
x = -1 y = 14 z = -13
x = 7 y = -99 z = 92
指折り数え計算すると
x = -97 y = 1370 z = -1273
x = -89 y = 1257 z = -1168
x = -81 y = 1144 z = -1063
x = -73 y = 1031 z = -958
x = -65 y = 918 z = -853
x = -57 y = 805 z = -748
x = -49 y = 692 z = -643
x = -41 y = 579 z = -538
x = -33 y = 466 z = -433
x = -25 y = 353 z = -328
x = -17 y = 240 z = -223
x = -9 y = 127 z = -118
x = -1 y = 14 z = -13
x = 7 y = -99 z = 92
x = 15 y = -212 z = 197
x = 23 y = -325 z = 302
x = 31 y = -438 z = 407
x = 39 y = -551 z = 512
x = 47 y = -664 z = 617
x = 55 y = -777 z = 722
x = 63 y = -890 z = 827
x = 71 y = -1003 z = 932
x = 79 y = -1116 z = 1037
x = 87 y = -1229 z = 1142
x = 95 y = -1342 z = 1247
のときに
92x+197y+205z=1をみたす(x,y,z)で｜ｘ＋ｙ＋ｚ｜= 0
結局、整数の縛りは必要なかったのだな。
整数であると書き忘れたのだろうと思って数えていったら最小値０の組み合わせが沢山みつかった。
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