numbertheory

Is this how I should complete my proof: By way of contradiction assume that 2k is the largest even integer. Now consider (2k)! (2k)! = (2k)(2k-1)(2k-2).......(k)(k-1)(k-2)......(2)(1) = 2[k(2k-1)(2k-2).......(k)(k-1)(k-2)......(2)(1)] = 2p, which is also an even integer. This contradicts...

Can anyone help me? The first digit of a 6-digit number is 1. This digit 1 is now moved from the first digit position to the end, so it becomes the last digit. The new 6-digit number is now 3 times larger than the original number. What are the last three digits of the original number? So far I...