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ParthKohli
 2 years ago
\[79^{79} \equiv N \pmod{100}\]\(N\) is a two digit number.
ParthKohli
 2 years ago
\[79^{79} \equiv N \pmod{100}\]\(N\) is a two digit number.

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ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Fermat's Little Theorem?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0\[79 \equiv 79 \equiv 0 \pmod{79} \]Which is kinda obvious.

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1And so we meet again.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Euler's Theorem says that \(\phi(79) = 79\) T_T

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah? I was talking to the modular maths problem XD LOL Jk

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1So anyway, 79^5 = 1(mod 100)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0How do you know again...

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.179^2 = 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)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0So \(79^{10} \equiv 1 \pmod{100}\)?

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah, that's true....

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1Meaning 79^70 = 1(mod 100), too :D

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

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

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0\[79^{70} \times 79^{5} \times 79^{4} \pmod{100}\]AH!

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1mhmm... 79^70 is 1 79^5 is 1 79^4, refer to the process we did earlier...

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0\[1 \times 1 \times 81 \pmod{100}\]

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah, that seems right :D
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