Efficient way to calculate A^B mod C, where B is high number

Asked Jan 06 '20 at 17:04

Active Jan 06 '20 at 19:26

Viewed 42 times

After reading Exponentiation by squaring , I know how to calculate certain (easy to express with in binary) exponents. However, I find this method inefficient to calculate on paper.

I have this following problem: 2 ^ 2000002 mod 41

What would be a "good" (efficient, quick, simple) way to approach and solve this type of problems, where the exponent is a very large number?

edited Jan 06 '20 at 17:06

asked Jan 06 '20 at 17:04

Milk and Honey

2

Fermat's little theorem? – Angina Seng Jan 06 '20 at 17:05
2

Note: that particular problem can be solved mentally since $2000002 \equiv 2\pmod {40}$ (visibly). – lulu Jan 06 '20 at 17:07
See modular order reduction. – Bill Dubuque Jan 06 '20 at 19:26

Efficient way to calculate A^B mod C, where B is high number

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