Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

BenjaminEE Group Title

Modular arithmetic. 21^20 = 1 (mod 100) From here it's simple to get that 21^(20+1) = 21 (mod 100) But what about 21^(20-1) = ? (mod 100) Is there a simple method for this?

  • one year ago
  • one year ago

  • This Question is Closed
  1. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \[21^{15} \cdot 21^4 \equiv 1 \cdot 81 \equiv 81 \pmod{100} \]

    • one year ago
  2. BenjaminEE Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks, but I'm looking for something more general. Like: \[p^ {n+1} = p \mod 100\] Where p^n = 1 mod 100

    • one year ago
  3. cahit Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[21==21\]

    • one year ago
  4. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    You have no way but to use the modulos.

    • one year ago
  5. cahit Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[21^2==41\]

    • one year ago
  6. cahit Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[21^3==61\]

    • one year ago
  7. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \[21^4 \equiv 81\]

    • one year ago
  8. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Yes, that is what I used to determine all the mods: pattern recognition. :-)

    • one year ago
  9. cahit Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    no until you reach 1 later on you can get the powr of 1

    • one year ago
  10. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    And write it in some crappy notation so that people think you are smart.

    • one year ago
  11. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Repeats every four terms.

    • one year ago
  12. cahit Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[21^5=1\]

    • one year ago
  13. BenjaminEE Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Well what if I have something a bigger repetition pattern? I don't want to brute force the problem.

    • one year ago
  14. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    You just have to find a power which is \(1\) or \(-1\) that thing. (thanks @terenzreignz!)

    • one year ago
  15. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \(1\) or \(-1\) modulo*

    • one year ago
  16. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    You always have Fermat's Little Theorem!

    • one year ago
  17. terenzreignz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Cute :) Then again, you could also express it as (20 + 1)^20 (mod 100) If that's any easier :D

    • one year ago
  18. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \[a^{b - 1} \equiv 1 \pmod{b}\]

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.