What is the solution to calculating 2^100 in ZZ11?

[Math10]

Homework Statement

Calculate 2^100 in ZZ₁₁.

Homework Equations

This is a Linear Algebra problem.

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
----------------------------
I think the answer is 1 since that's the remainder, am I right?

 

[.Scott]

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
----------------------------
I think the answer is 1 since that's the remainder, am I right?

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

 

[SammyS]

Homework Statement

Calculate 2^100 in ZZ₁₁.

Homework Equations

This is a Linear Algebra problem.

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
----------------------------
I think the answer is 1 since that's the remainder, am I right?

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:

https://www.wyzant.com/resources/answers/309299/calculate_2_100_in_zz11​

Here is a screen shot of the page that link takes you to.

Is that a coincidence ?

 

[berkeman]

Is that a coincidence ?

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.

 

[mfb]

I think the answer is 1 since that's the remainder, am I right?

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

 

[FactChecker]

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.

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.

 

[Math10]

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

Thank you so much!