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Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

Two Many

What is the least square number which commences with six two's?

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What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

Sept 03

Age 11 to 14 Challenge Level:

Another way of writing 1/5 !

Now look at first few powers and see what happens.