■リュカの問題の初等的証明(その6)
m=24k,24k+6,24k+12,24k+18
m=24k+1,24k+7,24k+13,24k+19
の場合まで絞られた.
m=3k→m^2=3(3k^2)
m=3k+1→m^2=3(k^2+2k)+1
m=3k−1→m^2=3(k^2−2k)+1
m=4k→m^2=4(4k^2)
m=4k±1→m^2=4(4k^2±2k)+1
m=4k±2→m^2=4(4k^2±4k+1)
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m=24k+6
m(m+1)(2m+1)/6=(4k+1)(24k+7)(48k+13)
24k+7=3 (mod4)
m=24k+12
m(m+1)(2m+1)/6=(4k+2)(24k+13)(48k+25)
4k+2=2 (mod4)
m=24k+18
m(m+1)(2m+1)/6=(4k+3)(24k+19)(48k+37)
4k+3=3 (mod4)
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m=24k+7
m(m+1)(2m+1)/6=(24k+7)(8k+1)(24k+7)
24k+7=3 (mod4)
m=24k+13
m(m+1)(2m+1)/6=(24k+13)(12k+7)(16k+9)
12k+7=3 (mod4)
m=24k+19
m(m+1)(2m+1)/6=(24k+19)(12k+10)(16k+13)
12k+10=2 (mod4)
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