Lastly - Well

What are the last two digits of 2^(2^2003)?

Counting Factors

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

Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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 $n$.