Every 8-digit number structured ABCXABCX, where A,B and C are not necessarily distinct, is divisible by 365 iff X equals either 5 or 0.

Why?

(In reply to Finishing the proof by Steve Herman)

Actually, my post proves both ways. The first paragraph proves that if it is divisible by 365, then it is divisible by 5. The second paragraph proves that if it is divisible by 5, then it is divisible by 365.

Posted by Math Man on 2011-10-24 16:35:10