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Find the remainder when $1^2 + 2^2 + 3^2 + 4^2 + \cdots + 132^2$ is divided by 11.

 

Find the remainder when $2 + 2^2 + 2^3 + 2^4 + \cdots + 2^{100}$ is divided by 7.

 

When the positive integer $n$ is divided by 6 the remainder is 5. When $n$ is divided by 10, the remainder is 9. What is the remainder when $n$ is divided by 30?

 

Thanks so much for the Help!

 

I really need help on these three problems, and all of these use Mods, and Im so confused what A mod is

 Oct 12, 2019
edited by FBIOPENUP  Oct 12, 2019
 #1
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sumfor(n, 1, 132, n^2) =775,390 mod 11 = 0 


sumfor(n, 1, 100, 2^n) = 2 5353012004 5645880299 3406410750 mod 7 = 2

 

n mod 6 =5, n mod 10 = 9, solve for n

 

n = 30 m + 29 and m =0, 1, 2, 3.......etc.

 

So, the smallest n = 29

 

29 mod 30 = 29

 Oct 12, 2019
 #2
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Thank you so much for the Help!

 Oct 12, 2019

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