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

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

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

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

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

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

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

terenzreignzBest 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

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

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

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

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

terenzreignzBest 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

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

terenzreignzBest 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

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

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