■2乗和が等しい数列(その5)

 うまく一意に定まらないので,答えから逆にたどることにした.

 {an}={1,4,6,7,10,11,13,16}

 {bn}={2,3,5,8,9,12,14,15}

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{an}={1,3,5,7,9,11,13,15}

{bn}={2,4,6,8,10,12,14,16}

{an^2}={1,9,25,49,81,121,169,225}

{bn^2}={4,16,36,64,100,144,196,256}

{cn}={bn^2−an^2}={3,−7,−11,15,−19,23,27,−31}=0

{an^3}={1,27,125,343,729,1331,2197,3375}}

{bn^3}={8,64,216,512,1000,1728,2744,4096}

{dn}={cn+1−cn}={30,−54,−78,102,−126,150,−174}=0

{cn}={bn^3−an^3}={7,−37,−91,169,−271,397,547,−721}=0

 4個ずつ{}するとき,両端の2項あるいは中央の2項が符号が変わるのだろうか?

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