本帖最后由 yangchuanju 于 2025-5-9 11:32 编辑
方程ac+a^3*b*c^4-a^3*b*c^3+a^2*b^2*c^2=10,14,22,26,……,都有整数解,5,7,11,13,……是合数还是素数?
2m 解组数 整数解
10 19 {{-10,0,-1},{-10,20,-1},{-5,0,-2},{-5,30,-2},{-2,0,-5},{-2,60,-5},{-1,-1,2},{-1,0,-10},{-1,3,2},{-1,110,-10},{1,-90,10},{1,-3,1},{1,0,10},{1,3,1},{2,-40,5},{2,0,5},{5,-10,2},{5,0,2},{10,0,1}}
14 21 {{-14,0,-1},{-14,28,-1},{-7,0,-2},{-7,42,-2},{-2,-2,1},{-2,0,-7},{-2,2,1},{-2,112,-7},{-1,0,-14},{-1,210,-14},{1,-182,14},{1,-5,-1},{1,-3,2},{1,0,14},{1,1,2},{1,3,-1},{2,-84,7},{2,0,7},{7,-14,2},{7,0,2},{14,0,1}}
22 17 {{-22,0,-1},{-22,44,-1},{-11,0,-2},{-11,66,-2},{-2,-1,-1},{-2,0,-11},{-2,5,-1},{-2,264,-11},{-1,0,-22},{-1,506,-22},{1,-462,22},{1,0,22},{2,-220,11},{2,0,11},{11,-22,2},{11,0,2},{22,0,1}}
26 19 {{-26,0,-1},{-26,52,-1},{-13,0,-2},{-13,78,-2},{-2,0,-13},{-2,364,-13},{-1,0,-26},{-1,702,-26},{1,-650,26},{1,-7,-2},{1,-5,1},{1,0,26},{1,1,-2},{1,5,1},{2,-312,13},{2,0,13},{13,-26,2},{13,0,2},{26,0,1}}
34 21 {{-34,0,-1},{-34,68,-1},{-17,0,-2},{-17,102,-2},{-2,-3,1},{-2,0,-17},{-2,3,1},{-2,612,-17},{-1,0,-34},{-1,1190,-34},{1,-1122,34},{1,-7,-1},{1,-4,2},{1,0,34},{1,2,2},{1,5,-1},{2,-544,17},{2,0,17},{17,-34,2},{17,0,2},{34,0,1}}
38 17 {{-38,0,-1},{-38,76,-1},{-19,0,-2},{-19,114,-2},{-2,0,-19},{-2,760,-19},{-1,0,-38},{-1,1482,-38},{1,-1406,38},{1,0,38},{2,-684,19},{2,-3,1},{2,0,19},{2,3,1},{19,-38,2},{19,0,2},{38,0,1}}
如果先生只对非0整数解,或者正整数解感兴趣,自己踢除就是了! |