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Number Theory Level 3

Find the remainder when 2 9 202 29^{202} is divided by 13.


The answer is 3.

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Akshat Sharda by Akshat Sharda , 21, India

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1 solution

Ankit Kumar Jain
Feb 28, 2016

2 9 202 ≡ 3 202 ≡ 3 201 × 3 ≡ 2 7 67 × 3 ≡ 1 67 × 3 ≡ 3 ( m o d 13 ) 29^{202}\equiv3^{202}\equiv3^{201}\times3\equiv27^{67}\times3\equiv1^{67}\times3\equiv3\pmod{13}

9 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Good observation of 3 3 ≡ 1 3^3 \equiv 1 to simplify the calculations.

Don't understand the first line

Md Sakir - 4 years, 5 months ago

Sorry....It must be mod 13 in the first line.

Ankit Kumar Jain - 4 years, 5 months ago

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