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    OlympiadHardNumber Theory7–9

    How many perfect squares between 11 and 20262026 end in the digit 66?

    Quantos quadrados perfeitos entre 11 e 20262026 terminam no algarismo 66?

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    Solution

    Step 1 of 3

    1. 1.A square ends in 66 exactly when its root ends in 44 or in 66, since only 424^{2} and 626^{2} end in 66.