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GR-HMS 2020 Problem 3

    On the board there are written in a row, the integers from 11 until 20302030 (included that) in an increasing order. We have the right of ''movement'' KK : We choose any two numbers a,ba,b that are written in consecutive positions and we replace the pair (a,b)(a,b) by the number (a−b)2020(a-b)^{2020} . We repeat the movement KK , many times until only one number remains written on the board. Determine whether it would be possible, that number to be: (i) 202020202020^{2020} (ii) 202120202021^{2020}

    Dataset text AI-MO AoPS. Quoted with source.

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    Locator gr-hms/2020/p3 · Tag C2S030XB07 · Edit this page on GitHub · Keys: j next, k previous