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# remainder

Find the remainder when (15)raised to 2010 + (16)raised to 2011 is divided by 7.

Note by Ronak Pawar
4 years, 1 month ago

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Since 15 is congruent to 1 modulo 7, 15^2010 is congruent to 1^2010 = 1 modulo 7 and 16 is congruent to 2 modulo 7, 16^2011 is congruent to 2^2011 modulo 7. Imagine that 2^3 is congruent to 1 modulo 7, then 2^2010 is congruent to 1^2010 = 1 modulo 7 and hence, 2^2011 is congruent to 2 modulo 7. Adding the remainders (since positive congruence), 15^2010 + 16^2011 is congruent to 1 + 2 = 3.

- 4 years, 1 month ago

Do it by modulo function.

- 3 years, 8 months ago

Looks like you have a modular arithmetic problem there - have a look at the 2 technique trainer articles Modular Arithmetic and Euler's Theorem first, and see how you go.

- 4 years, 1 month ago

4

- 4 years, 1 month ago