150824(6)

Ruby


どの２つの和も立方数(16)

異なる自然数a, b, c, d (a < b < c < d)が

a + b = u^3,
a + c = v^3,
a + d = w^3,
b + c = x^3,
b + d = y^3,
c + d = z^3,

w^3 < x^3

を満たすとき、

a' = (a + b + c - d) / 2,

b' = (a + b - c + d) / 2,

c' = (a - b + c + d) / 2,

d' = (- a + b + c + d) / 2

とおくと、

0< a < a' < b' < c' < d'

a' + b' = u^3,

a' + c' = v^3,
a' + d' = x^3,
b' + c' = w^3,
b' + d' = y^3,
c' + d' = z^3

が成り立つ。

よって、この変換でa', b', c', d'が自然数なら、

1から2の例が作れるわけである。

# aryに1の例を代入

def t(ary)

  a, b, c, d = ary

  [(a + b + c - d) / 2, (a + b - c + d) / 2, (a - b + c + d) / 2, (- a + b + c + d) / 2]

end

p t([16955834122364, 117750072394364, 128741810605636, 163827996114820])

p t([29426395971164, 750836969211164, 1140146474684836, 1719392658620836])

出力結果

[49809860503772, 84896046012956, 95887784224228, 196682022496228]

[100508590623164, 679754774559164, 1069064280032836, 1790474853272836]