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Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

N000ughty Thoughts

How many noughts are at the end of these giant numbers?

Mod 3

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

Big Powers

Age 11 to 16Challenge Level

What determines whether a number is divisible by $5$ or not?

Find: $3^{1}, 3^{2}, 3^{3}, 3^{4}, 3^{5}, 3^{6}, 3^{7}, 3^{8}, 3^{9} \ldots$

What do you notice?

Find: $4^{1}, 4^{2}, 4^{3}, 4^{4}, 4^{5}, 4^{6}, 4^{7}, 4^{8}, 4^{9} \ldots$

What do you notice?