# Homework Help: Calculate 2^100 in ZZ11?

1. May 14, 2017

### Math10

1. The problem statement, all variables and given/known data
Calculate 2^100 in ZZ11.

2. Relevant equations
This is a Linear Algebra problem.

3. The attempt at a solution
Here's my work:
2^5=32=-1 mod 11
2^10=1 mod 11
2^100=1 mod 11
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I think the answer is 1 since that's the remainder, am I right?

2. May 14, 2017

### .Scott

You are correct. Note also that 2^10 = 1024 = 93*11 + 1.

3. May 14, 2017

### SammyS

Staff Emeritus
I gather that you are referring to ℤ11 .

In trying to see if ZZ was the same as ℤ, I came across the following link:
Here is a screen shot of the page that link takes you to.

Is that a coincidence ?

4. May 16, 2017

### Staff: Mentor

It's generally okay if they are posting in a couple of places looking for help. As long as they don't post links to the other forums here.

5. May 16, 2017

### Staff: Mentor

If you are just interested in checking the answer, WolframAlpha can do that - the answer is 1.

6. May 16, 2017

### FactChecker

I think it would only be polite if a good solution given in one forum were put into the other threads. But that presents other issues.

7. May 18, 2017