Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
ParthKohli
Group Title
\[79^{79} \equiv N \pmod{100}\]\(N\) is a two digit number.
 one year ago
 one year ago
ParthKohli Group Title
\[79^{79} \equiv N \pmod{100}\]\(N\) is a two digit number.
 one year ago
 one year ago

This Question is Closed

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Fermat's Little Theorem?
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
\[79 \equiv 79 \equiv 0 \pmod{79} \]Which is kinda obvious.
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
And so we meet again.
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Euler's Theorem says that \(\phi(79) = 79\) T_T
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Yeah ;)
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Yeah? I was talking to the modular maths problem XD LOL Jk
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
So anyway, 79^5 = 1(mod 100)
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
How do you know again...
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
79^2 = 6241 = 41(mod 100) 79^3 = (41)(79)(mod 100) = 39(mod 100) 79^4 = (39)(79)(mod 100) = 81(mod 100) 79^5 = (81)(79)(mod 100) = 99(mod 100) = 1(mod 100)
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
So \(79^{10} \equiv 1 \pmod{100}\)?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Yeah, that's true....
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Meaning 79^70 = 1(mod 100), too :D
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Okay, oh.
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
So does that mean \(79^{80} \equiv 1 \pmod {100}\)
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Ah, yeah.
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Yes... But it's 79^79 you want, right? 79^75 = 1(mod 100)
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
\[79^{70} \times 79^{5} \times 79^{4} \pmod{100}\]AH!
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
mhmm... 79^70 is 1 79^5 is 1 79^4, refer to the process we did earlier...
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
\[1 \times 1 \times 81 \pmod{100}\]
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Yeah, that seems right :D
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
\[19\pmod{100}\]
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Bingo... :
 one year ago
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
 Engagement 19 Mad Hatter
 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.