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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?
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.
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 $n$.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.