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What fractions can you find between the square roots of 65 and 67?

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

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To help explain it is worth considering the journey from the bottom up.