Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.7 AIME Find the answer

45. Find eight natural numbers $a_{i}$ such that

$\sqrt{\sqrt{a_{1}}-\sqrt{a_{1}-1}}+\ldots+\sqrt{\sqrt{a_{8}}-\sqrt{a_{8}-1}}=2$

Solution

91.45. Consider the numbers $a_{h}=(2 k+1)^{2}$ for $k=1,2, \ldots, 8$ .

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