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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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Repeaters

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.

Differences

Age 11 to 14 Challenge Level:

    Pick three test values - calculate differences (why are only three listed?) - and then the product. Can you find an exception? The question is "Why not?".

    The second half of the question is about multiples of three. Can you 'categorise' numbers in terms of their relationship to mulltiples of three and how does this help?

    Have you seen the problem Take Three from Five ?