What is the remainder 5^{1000} divided by 26?

  • Option 1)

    24

  • Option 2)

    5

  • Option 3)

    25

  • Option 4)

    21

  • Option 5)

    1

Answers (1)

\frac{5^{1000}}{26}

\frac{5^{1}}{26}=remainder 5

\frac{5^{2}}{26}=remainder 25

\frac{5^{3}}{26}=remainder 21

\frac{5^{4}}{26}=remainder 1

Cyclicity of 5 is 4

0 remainder means last term of cycle

Remainder=1

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