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关于“数学”的对话(15)
(接(14))
乙:还有:
(aa,ab,ac)^2+(ab,ac,aa)^2+(ac,aa,ab)^2
=492^2+924^2+249^2=1157841
=(ca,cb,cc)^2+(cb,cc,ca)^2+(cc,ca,cb)^2
=816^2+168^2+681^2=1157841,
(ba,bb,bc)^2+(bb,bc,ba)^2+(bc,ba,bb)^2
=357^2+573^2+735^2=996003,
(aa,ba,ca)^2+(ba,ca,aa)^2+(ca,aa,ba)^2
=438^2+384^2+843^2=1049949
=(ac,bc,cc)^2+(bc,cc,ac)^2+(cc,ac,bc)^2
=276^2+762^2+627^2=1049949,
(ab,bb,cb)^2+(bb,cb,ab)^2+(cb,ab,bb)^2
=951^2+519^2+195^2=1211787,
(aa,bb,cc)^2+(bb,cc,aa)^2+(cc,aa,bb)^2
=456^2+564^2+645^2=942057,
(ca,bb,ac)^2+(bb,ac,ca)^2+(ac,ca,bb)^2
=852^2+528^2+285^2=1085913,
行和列中不含“
而且,含“
甲:还有:
(aa,ab,ac)^3+(ab,ac,aa)^3+(ac,aa,ab)^3
=492^3+924^3+249^3=1923422761,
(ca,cb,cc)^3+(cb,cc,ca)^3+(cc,ca,cb)^3
=816^3+168^3+681^3=863901369,
(ba,bb,bc)^3+(bb,bc,ba)^3+(bc,ba,bb)^3
=357^3+573^3+735^3=631187785,
(aa,ba,ca)^3+(ba,ca,aa)^3+(ca,aa,ba)^3
=438^3+384^3+843^3=739727883,
(ac,bc,cc)^3+(bc,cc,ac)^3+(cc,ac,bc)^3
=276^3+762^3+627^3=710467187,
(ab,bb,cb)^3+(bb,cb,ab)^3+(cb,ab,bb)^3
=951^3+519^3+195^3=1007298584,
(aa,bb,cc)^3+(bb,cc,aa)^3+(cc,aa,bb)^3
=456^3+564^3+645^3=542551085,
(ca,bb,ac)^3+(bb,ac,ca)^3+(ac,ca,bb)^3
=852^3+528^3+285^3=888817285,
行、列和斜的各3个循环的3位数的立方之和也就全都不相等。
(未完待续)
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