Indices

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?

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?

How many zeros are there at the end of $3^4 \times 4^5 \times 5^6$?

Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?

How much money did the Queen give away in pence as a power of 2?

The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!

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

Find 180 to the power 59 (mod 391) to crack the code. To find the secret number with a calculator we work with small numbers like 59 and 391 but very big numbers are used in the real world for this.