remainder

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

#HelpMe! #Math #Opinions

Note by Ronak Pawar
7 years, 6 months ago

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Comments

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.

Answer: 3 is the remainder.

John Ashley Capellan - 7 years, 6 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.

Ryan Carson - 7 years, 6 months ago

Do it by modulo function.

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