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.
(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 20130510 14:47:46 