 | 2005/10/25(Tue) 14:32:43 編集(投稿者)
a=27とすると
133^5+110^5+84^5+27^5
=(5a-2)^5+(4a+2)^5+(3a+3)^5+a^5
=3125a^5-6250a^4+5000a^3-2000a^2+400a-32
+1024a^5+2560a^4+2560a^3+1280a^2+320a+32
+243a^5+1215a^4+2430a^3+2430a^2+1215a+243
+a^5
=4393a^5-2475a^4+9990a^3+1710a^2+1935a+243
=(163a-8)a^5-(92a-9)a^4+370a・a^3+(63a+9)a^2+(72a-9)a+9a
=163a^6-100a^5+379a^4+63a^3+81a^2
=(6a+1)a^6-(4a-8)a^5+(14a+1)a^4+(2a+9)a^3+3a・a^2
=6a^7-3a^6+22a^5+3a^4+12a^3
=a^3(6a^4-3a^3+22a^2+3a+12)
=a^3(6a^4-3a^3+21a^2+30a+12)
=3a^3(2a^4-a^3+7a^2+10a+4)
=3a^3(a^4+26a^3+7a^2+10a+4)
=3a^3(a^4+20a^3+169a^2+10a+4)
=3a^3(a^4+20a^3+150a^2+523a+4)
=3a^3(a^4+20a^3+150a^2+500a+625)
=3a^3(a+5)^4
=3・(3^3)^3・(2^5)^4
=(2^4・3^2)^5
=144^5
∴133^5+110^5+84^5+27^5=144^5
# 直接計算した方が早いかも。
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