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    Daily ChallengeHardNumber Theory

    What is the remainder when 2102^{10} is divided by 7?

    Qual é o resto quando 2102^{10} é dividido por 7?

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    Solution

    23≡1(mod7)2^{3} \equiv 1 \pmod{7}, so 210=29×2=(23)3×2≡1×2=2(mod7)2^{10} = 2^{9} \times 2 = (2^{3})^{3} \times 2 \equiv 1 \times 2 = 2 \pmod{7}