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### Number and algebra

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# Power Countdown

Try writing the larger numbers as powers of smaller numbers, and the smaller numbers as roots of larger ones.

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### Root to Poly

### Consecutive Squares

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Age 14 to 16

Challenge Level

- Problem
- Getting Started
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Try writing the larger numbers as powers of smaller numbers, and the smaller numbers as roots of larger ones.

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?