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Find largest possible integer value of a such that
2+a2+a2+a2+...>aaaa...2+\cfrac{a}{2+\cfrac{a}{2+\cfrac{a}{2+...}}}>\sqrt{a\sqrt{a\sqrt{a\sqrt{a...}}}}2+2+2+2+...aaa>aaaa...
This is part of the set Fun With Problem-Solving.
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