160126

Ruby


「和の２乗 = ３乗の和」となる組合せ(4)

1≦s1≦s2≦･･･≦s(n-1)≦sn≦n

なる自然数の組[s1,s2,･･･,s(n-1),sn]
において関係式
2(s1+s2+･･･+s(n-1)+sn)^4
=(s1^5+s2^5+･･･+s(n-1)^5+sn^5)+(s1^7+s2^7+･･･+s(n-1)^7+sn^7)
が成立する組合せ
についてもう少し調べてみた。

(2..18).each{|n|
  a_ary = []
  (1..n).to_a.repeated_combination(n){|c|
    a_ary << c if (c.inject(:+) ** 4) * 2 == c.map{|i| i ** 5}.inject(:+) + c.map{|i| i ** 7}.inject(:+)
  }
  p a_ary
}

出力結果
[[1, 2]]
[[1, 2, 3]]
[[1, 2, 3, 4]]
[[1, 2, 3, 4, 5]]
[[1, 2, 3, 4, 5, 6]]
[[1, 2, 3, 4, 5, 6, 7]]
[[1, 2, 3, 4, 5, 6, 7, 8]]
[[1, 2, 3, 4, 5, 6, 7, 8, 9]]
[[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]
[[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]
[[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]]
[[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]]
[[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]]
[[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]]
[[1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 5, 7, 9, 9, 10, 12], [1, 1, 1, 2, 3, 4, 4, 5, 7, 7, 8, 8, 8, 11, 12, 14], [1, 1, 1, 7, 8, 9, 10, 11, 11, 14, 14, 15, 16, 16, 16, 16], [1, 2, 2, 3, 3, 4, 6, 8, 9, 12, 12, 12, 12, 12, 13, 16], [1, 2, 3, 4, 4, 5, 6, 9, 9, 9, 11, 12, 14, 14, 15, 15], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [2, 2, 2, 2, 4, 4, 4, 5, 7, 7, 8, 10, 12, 13, 13, 14], [2, 4, 4, 4, 4, 4, 6, 6, 7, 7, 9, 9, 10, 10, 12, 16], [4, 4, 4, 4, 6, 6, 6, 6, 9, 9, 10, 10, 11, 12, 16, 16]]
[[1, 2, 2, 3, 4, 5, 6, 6, 8, 9, 10, 11, 11, 11, 11, 13, 17], [1, 2, 3, 3, 3, 5, 8, 8, 8, 9, 9, 9, 10, 11, 12, 16, 16], [1, 2, 3, 4, 5, 6, 6, 6, 6, 6, 6, 7, 8, 9, 9, 11, 16], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [1, 4, 4, 4, 4, 6, 6, 6, 13, 14, 14, 14, 15, 16, 16, 16, 16], [2, 2, 3, 3, 5, 5, 5, 5, 10, 11, 11, 14, 14, 14, 14, 16, 16], [2, 2, 3, 6, 6, 6, 8, 8, 10, 12, 13, 14, 16, 16, 16, 16, 17], [4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 7, 8, 10, 10, 10, 16], [4, 4, 4, 4, 5, 5, 5, 7, 8, 12, 12, 14, 15, 15, 15, 16, 17]]
[[1, 1, 1, 1, 1, 2, 3, 6, 6, 6, 7, 7, 10, 11, 11, 13, 13, 15], [1, 1, 1, 2, 2, 3, 4, 4, 5, 5, 7, 7, 8, 8, 8, 8, 10, 15], [1, 1, 1, 2, 3, 3, 4, 6, 7, 10, 10, 10, 11, 12, 12, 13, 16, 16], [1, 1, 1, 3, 3, 4, 4, 5, 7, 7, 11, 12, 12, 12, 12, 13, 14, 17], [1, 1, 1, 3, 5, 5, 7, 8, 10, 10, 10, 11, 15, 15, 15, 16, 16, 17], [1, 1, 1, 4, 6, 6, 6, 6, 7, 7, 7, 7, 9, 9, 11, 11, 14, 17], [1, 1, 2, 2, 2, 2, 2, 6, 6, 6, 10, 10, 10, 11, 13, 13, 15, 15], [1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 10, 11, 12, 13], [1, 1, 2, 2, 2, 3, 3, 7, 7, 9, 10, 11, 12, 12, 12, 13, 14, 17], [1, 1, 2, 2, 4, 4, 4, 6, 7, 9, 9, 11, 11, 11, 12, 12, 15, 17], [1, 1, 2, 3, 4, 8, 8, 8, 8, 8, 8, 14, 14, 15, 15, 16, 16, 17], [1, 1, 2, 4, 4, 4, 7, 7, 7, 8, 9, 12, 12, 13, 15, 16, 16, 16], [1, 1, 2, 4, 4, 4, 7, 7, 7, 8, 10, 10, 11, 12, 13, 13, 13, 18], [1, 1, 3, 3, 5, 7, 8, 12, 12, 14, 14, 15, 15, 16, 17, 17, 18, 18], [1, 1, 3, 4, 4, 4, 4, 5, 6, 6, 7, 7, 8, 10, 11, 13, 14, 16], [1, 1, 3, 4, 5, 7, 9, 10, 11, 11, 14, 14, 14, 16, 16, 17, 18, 18], [1, 2, 2, 2, 4, 4, 4, 4, 6, 6, 6, 7, 10, 10, 10, 10, 13, 16], [1, 2, 2, 3, 4, 4, 8, 8, 11, 11, 11, 11, 13, 14, 14, 17, 17, 17], [1, 2, 3, 3, 4, 5, 7, 7, 8, 8, 9, 9, 9, 9, 10, 15, 15, 17], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [1, 3, 3, 3, 4, 7, 7, 8, 9, 9, 14, 14, 14, 15, 16, 17, 17, 17], [1, 3, 3, 3, 6, 8, 8, 8, 8, 8, 8, 9, 12, 12, 12, 13, 17, 18], [1, 3, 4, 4, 4, 6, 10, 14, 14, 14, 14, 15, 16, 17, 18, 18, 18, 18], [1, 4, 4, 4, 4, 4, 5, 6, 6, 10, 10, 14, 14, 15, 16, 16, 16, 16], [2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 5, 6, 6, 10, 10, 11, 14, 14], [2, 2, 2, 2, 3, 4, 5, 6, 6, 10, 10, 10, 10, 11, 13, 14, 15, 17], [2, 2, 2, 2, 5, 6, 6, 6, 7, 8, 8, 10, 10, 12, 13, 16, 16, 16], [2, 2, 2, 5, 6, 7, 7, 7, 8, 9, 10, 11, 12, 12, 15, 17, 17, 17], [2, 2, 3, 4, 4, 6, 6, 6, 6, 8, 9, 13, 14, 14, 14, 14, 14, 18], [2, 2, 4, 4, 4, 4, 5, 6, 7, 9, 12, 14, 14, 14, 15, 16, 16, 17], [2, 3, 3, 4, 6, 8, 9, 9, 9, 9, 9, 14, 15, 15, 16, 16, 18, 18], [2, 3, 4, 4, 5, 5, 7, 7, 8, 8, 8, 9, 9, 10, 10, 12, 15, 18], [2, 3, 4, 6, 6, 7, 7, 8, 12, 12, 12, 14, 16, 17, 17, 17, 18, 18], [2, 3, 5, 5, 5, 5, 6, 6, 6, 6, 7, 11, 12, 14, 14, 14, 14, 18], [2, 4, 4, 4, 4, 4, 6, 7, 10, 10, 12, 13, 13, 16, 16, 16, 16, 18], [2, 6, 6, 6, 6, 6, 6, 7, 7, 9, 9, 12, 15, 15, 16, 17, 17, 18], [3, 3, 4, 4, 6, 6, 7, 7, 12, 12, 12, 13, 15, 17, 17, 17, 17, 18], [3, 3, 4, 6, 7, 9, 9, 9, 9, 9, 9, 11, 11, 13, 15, 18, 18, 18], [3, 4, 4, 4, 5, 5, 6, 7, 8, 11, 13, 14, 14, 14, 14, 16, 18, 18], [3, 5, 5, 5, 7, 7, 7, 13, 15, 16, 17, 18, 18, 18, 18, 18, 18, 18]]