Modulo

Number Theory Level 2

What is the remainder when 3 8 101 38^{101} is divided by 13?


The answer is 12.

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Munem Shahriar
Sep 6, 2017

38 ≡ − 1 38 \equiv -1 ( mod 13 ) (\text{mod 13})

3 8 101 ≡ ( − 1 ) 101 ≡ − 1 ≡ 12 ( mod 13 ) 38^{101} \equiv (-1)^{101} \equiv -1 \equiv 12 ( \text{mod 13})

Hence the remainder is 12 \boxed{12}

4 Helpful 0 Interesting 0 Brilliant 0 Confused

How did you do the mod without spacing? Can you show me the code for the mod function?

Yajat Shamji - 11 months, 2 weeks ago

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