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)

Bravo, Math Man! Your proof looks great to me. Nice work!

All of Broll's results are in fact on the closed set that Broll articulated.

1,1,4,6 corresponds to 2,3,12,12

1,2,2,5 corresponds to 2,5,5,10

1,2,6,9 " 2,3,9,18

1,3,4,4 " 3,3,4,12

1,3,8,12 " 2,3,8,24

1,4,5,10 " 2,4,5,20

1,6,14,21 " 2,3,7,42

2,3,10,15 " 2,3,10,15

The last of these is particularly interesting, because a,b,c,d = z,y,x,w. This is also the only one where the LCM is divisible by both 3 and 5. Coincidence? I think not.

*Edited on ***May 11, 2013, 11:41 am**