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What an Odd Fact(or)

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

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Counting Factors

Is there an efficient way to work out how many factors a large number has?

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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.


Age 11 to 14 Challenge Level:

What is the remainder of $2^{2002}\div 7?$

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What happens with different powers of $2$?

Try to explain the mathematics behind what you discover.