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1) What is the remainder when \(2013^{2013} \) is divided by 13?

 

2) What is the remainder when \(17^{77} \) is divided by 35?

 

3) For how many positive integers n less than 100 is \(5^n+8^{n+1}+13^{n+2} \) a multiple of 6?

 

4) Find the smallest positive multiple of 21 that has no digit larger than 1.

 Oct 24, 2020
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1 - 2013^2013 mod 13 = 8 - the remainder.

 

2 - 17^77 mod 35 = 12 - the remainder

 

3 - There are NO "n" less than 100 that are multiples of 6.

 

4 - The smallest positive multiple of 21 that has no digits larger than 1 ==101010

 Oct 24, 2020

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