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ParthKohli Group Title

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

  • one year ago
  • one year ago

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  1. ParthKohli Group Title
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    Fermat's Little Theorem?

    • one year ago
  2. ParthKohli Group Title
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    \[79 \equiv 79 \equiv 0 \pmod{79} \]Which is kinda obvious.

    • one year ago
  3. terenzreignz Group Title
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    And so we meet again.

    • one year ago
  4. ParthKohli Group Title
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    Euler's Theorem says that \(\phi(79) = 79\) T_T

    • one year ago
  5. ParthKohli Group Title
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    Yeah ;-)

    • one year ago
  6. terenzreignz Group Title
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    Yeah? I was talking to the modular maths problem XD LOL Jk

    • one year ago
  7. terenzreignz Group Title
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    So anyway, 79^5 = -1(mod 100)

    • one year ago
  8. ParthKohli Group Title
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    How do you know again...

    • one year ago
  9. terenzreignz Group Title
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    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
  10. ParthKohli Group Title
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    So \(79^{10} \equiv 1 \pmod{100}\)?

    • one year ago
  11. terenzreignz Group Title
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    Yeah, that's true....

    • one year ago
  12. terenzreignz Group Title
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    Meaning 79^70 = 1(mod 100), too :D

    • one year ago
  13. ParthKohli Group Title
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    Okay, oh.

    • one year ago
  14. ParthKohli Group Title
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    So does that mean \(79^{80} \equiv 1 \pmod {100}\)

    • one year ago
  15. ParthKohli Group Title
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    Ah, yeah.

    • one year ago
  16. terenzreignz Group Title
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    Yes... But it's 79^79 you want, right? 79^75 = -1(mod 100)

    • one year ago
  17. ParthKohli Group Title
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    \[79^{70} \times 79^{5} \times 79^{4} \pmod{100}\]AH!

    • one year ago
  18. terenzreignz Group Title
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    mhmm... 79^70 is 1 79^5 is -1 79^4, refer to the process we did earlier...

    • one year ago
  19. ParthKohli Group Title
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    \[1 \times -1 \times 81 \pmod{100}\]

    • one year ago
  20. terenzreignz Group Title
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    Yeah, that seems right :D

    • one year ago
  21. ParthKohli Group Title
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    \[19\pmod{100}\]

    • one year ago
  22. terenzreignz Group Title
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    Bingo... :|

    • one year ago
  23. ParthKohli Group Title
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    :-D

    • one year ago
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