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What is the remainder when 7^100 is divided by 50?

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What is the remainder when 7^100 is divided by 50?

by Max@Math Revolution » Thu Jun 13, 2019 11:03 pm

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What is the remainder when 7^100 is divided by 50?

A. 1
B. 3
C. 5
D. 7
E. 49
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by Max@Math Revolution » Sun Jun 16, 2019 10:01 pm
When we compute with remainders, we can either take the remainder first and then compute, or compute first and then take the remainder.

7^2 = 49 has remainder 49 when it is divided by 50.
When numbers are divided by 50, a remainder of 49 can be thought of as a remainder of -1.
Therefore, 7^100 ~ (7^2)^50 ~ (49)^50 ~ (-1)^50 ~ 1.

When 7^100 is divided by 50, it has remainder 1.

Therefore, A is the answer. 
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