# Resources tagged with: Indices

### There are 6 results

Broad Topics >

Algebraic expressions, equations and formulae > Indices

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

##### Age 11 to 14 Challenge Level:

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

##### Age 11 to 14 Challenge Level:

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?

##### Age 11 to 18

We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.

##### Age 11 to 16

This article for students and teachers tries to think about how
long would it take someone to create every possible shuffle of a
pack of cards, with surprising results.