Evaluate $10^{20231016} \pmod{1021}$ (Hint : $1021$ is a prime)

Asked Oct 07 '23 at 14:04

Active Oct 07 '23 at 14:23

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Evaluate $10^{20231016} \pmod{1021}$ (Hint : $1021$ is a prime)

Does anyone know how to solve this question?

I found that $10^{20231016} \pmod{1021}$ is equivalent to $10^{336} \pmod{1021}$ using Fermat's Little Theorem, but I don't know how to handle it in the following steps.

edited Oct 07 '23 at 14:23

Anne Bauval

49,005

asked Oct 07 '23 at 14:04

Qualis ab incepto

2

Try exponentiation by repeated squaring? – peterwhy Oct 07 '23 at 14:13
1

20231016 looks suspiciously like a date that occurs later this month. This question may be part of an ongoing competition. – Daniel Mathias Oct 07 '23 at 14:58
@peterwhy I’ll give it a try. – Qualis ab incepto Oct 07 '23 at 15:29
@DanielMathias Because it is my collage homework which deadline is on October 16th. – Qualis ab incepto Oct 07 '23 at 15:49
my question was solved.Thanks everyone! – Qualis ab incepto Oct 15 '23 at 15:26

Evaluate $10^{20231016} \pmod{1021}$ (Hint : $1021$ is a prime)

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