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Rationals Between

What fractions can you find between the square roots of 56 and 58?

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Root to Poly

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

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Consecutive Squares

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

Integer Indices

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Given that $5^j + 6^k + 7^l + 11^m = 2006$ where $j$, $k$, $l$ and $m$ are different non-negative integers, what is the value of $j+k+l+m$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.



This problem is taken from the UKMT Mathematical Challenges.
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