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(2): Infinite examples, no proof yet. by Jer)

Maybe I don't understand your question, Jer, but it is easy to prove that abcd must be a multiple of 2.

Assume that the LCM is odd.

Then a, b, c and d are all odd.

Then a + b + c + d is even. But a + b + c + d is the LCM, so this is a contradiction.

Therefore, the initial assumption is wrong, and the LCM must be even.