■729と1729(その21)
[1](9n^4)^3+(9n^3+1)^3=(9n^4+3n)^3+1
n=1のとき,9^3+10^3=12^3+1
n=−1のとき,9^3+(−8)3=6^3+1=217
[2](9n^4)^3+(1−9n^3)^3+(3n−9n^4)^3=1
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[1]左辺=9^3n^12+9^3n^9+3・9^2n^6+3・9n^3+1
右辺=9^3n^12+9^3n^9+3・9^2n^6+3・9n^3+1
[2]左辺=9^3n^12+1-3・9n^3+3・9^2n^6-9^3n^9+27n^3-3・9^2n^6+9^3n^9-9^3n^12=1=右辺
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