９倍自己再現数の末尾は４，５，９のいすれかである．

＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝

　　９（０９）^2＝７２９

　　９（１９）^2＝３２４９

　　９（２９）^2＝７５６９

　　９（３９）^2＝１３６８９

　　９（４９）^2＝２１６０９

　　９（５９）^2＝３１３２９

　　９（６９）^2＝４２８４９

　　９（７９）^2＝５６１６９

　　９（８９）^2＝７１２８９・・・９倍保型数

　　９（９９）^2＝８８２０９

　　９（０８９）^2＝７１２８９

　　９（１８９）^2＝３２１４８９

　　９（２８９）^2＝７５１６８９

　　９（３８９）^2＝１３６１８８９

　　９（４８９）^2＝２１５２０８９

　　９（５８９）^2＝３１２２２８９

　　９（６８９）^2＝４２７２４８９

　　９（７８９）^2＝５６０２６８９

　　９（８８９）^2＝７１１２８８９・・・９倍保型数

　　９（９８９）^2＝８８０３０８９

　　９（０８８９）^2＝７１１２８８９

　　９（１８８９）^2＝３２１１４８８９

　　９（２８８９）^2＝７５１１６８８９

　　９（３８８９）^2＝１３６１１８８８９

　　９（４８８９）^2＝２１５１２０８８９

　　９（５８８９）^2＝３１２１２２８８９

　　９（６８８９）^2＝４２７１２４８８９

　　９（７８８９）^2＝５６０１２６８８９

　　９（８８８９）^2＝７１１１２８８８９・・・９倍保型数

　　９（９８８９）^2＝８８０１３０８８９

＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝

［まとめ］この結果は（その１５）（その１６）の

　　ａ0＝７２９＝２７^2＝３^2・９^2

　　ａ1＝７１２８９＝２６７^2＝３^2・８９^2

　　ａ2＝７１１２８８９＝２６６７^2＝３^2・８８９^2

　　ａ3＝７１１１２８８８９＝２６６６７^2＝３^2・８８８９^2

　　ａ4＝７１１１１２８８８８９＝２６６６６７^2＝３^2・８８８８９^2

　　ａ5＝７１１１１１２８８８８８９＝２６６６６６７^2＝３^2・８８８８８９^2

と同値である．

＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝