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.

(1,2,2,5)  fits, did not look for other examples.

If there are none - then this is a proof.

If one lists  ALL   examples that fit - it is ok as well.

I have nothing to add.

Posted by Ady TZIDON on 2013-04-28 09:24:25