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Diggits

Can you find what the last two digits of the number $4^{1999}$ are?

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Two Many

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

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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?

Like Powers

Stage: 3 Challenge Level: Challenge Level:1

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 $n$.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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