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 Dark Divisibility (Posted on 2013-04-27)
The natural numbers a,b,c,d are such that their least common multiple equals a+b+c+d. Prove that abcd is divisible by 3 or by 5.

 No Solution Yet Submitted by Danish Ahmed Khan Rating: 5.0000 (2 votes)

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 re(2): Proof | Comment 16 of 18 |
(In reply to re: Proof by broll)

w<=x<=y<=z means a>=b>=c>=d.

{d, c, b, a}->{a, b, c, d}->{w, x, y, z}
{1, 1, 4, 6}->{6, 4, 1, 1}->{2, 3, 12, 12}
{1, 2, 2, 5}->{5, 2, 2, 1}->{2, 5, 5, 10}
{1, 2, 6, 9}->{9, 6, 2, 1}->{2, 3, 9, 18}
{1, 4, 5, 10}->{10, 5, 4, 1}->{2, 4, 5, 20}
{1, 3, 8, 12}->{12, 8, 3, 1}->{2, 3, 8, 24}
{1, 6, 14, 21}->{21, 14, 6, 1}->{2, 3, 7, 42}
{2, 3, 10, 15}->{15, 10, 3, 2}->{2, 3, 10, 15}

 Posted by Math Man on 2013-05-10 14:47:46

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