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

Power Crazy

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?

Largest Number

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

Like Powers

Age 11 to 14 Challenge Level:

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 $n$.