Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?
Is there an efficient way to work out how many factors a large number has?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
I used a spreadsheet to get the sense of what was happening. It is easy to see the pattern but the question is asking you to try to explain it!