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Thread: number theory

  1. September 22nd 2012, 09:12 AM #1
    Petrus
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    number theory

    i prob post on wrong sector but idk where i should post it, sorry
    the quest is :
    Which (positive) residual obtained when 11^30+5^31-6 divided by 24?

    i have got this far
    11^30=(11^2)^15=121^15 ==1^15 (mod 24)
    i cant solve rest :S
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  2. September 22nd 2012, 09:51 AM #2
    MaxJasper
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    Lightbulb Re: number theory

    Quote Originally Posted by Petrus View Post
    i prob post on wrong sector but idk where i should post it, sorry
    the quest is :
    Which (positive) residual obtained when 11^30+5^31-6 divided by 24?

    i have got this far
    11^30=(11^2)^15=121^15 ==1^15 (mod 24)
    i cant solve rest :S
    \left(11^{30}+5^{31}-6\right) \bmod 24 =11^{30}\text{mod} 24 +5^{31}\text{mod} 24 -6 \bmod 24=11^{2+28}\text{mod} 24+5^{1+30}\text{mod24}-6=121*11^{28}\text{mod24}+5*5^{30}\text{mod} 24-6 \bmod 24 = 1+5-6=0
    Last edited by MaxJasper; September 22nd 2012 at 10:15 AM.
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  3. September 22nd 2012, 10:01 AM #3
    Petrus
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    Re: number theory

    Sorry but i did not get it with 5^31
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  4. September 22nd 2012, 11:26 AM #4
    Soroban
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    Re: number theory

    Hello, Petrus!

    You are on the right track . . .

    \text{What is the remainder when }11^{30}+5^{31}-6\text{ is divided by 24?}

    11^{30} \;=\; (11^2)^{15} \;=\;(121)^{15} \;\equiv\; 1^{15}\text{ (mod 24)} \;\equiv\;1\text{ (mod 24)}

    5^{31} \;=\;5\cdot5^{30} \;=\;5(5^2)^{15} \;=\;5(25)^{15} \;\equiv\; 5(1)^{15}\text{ (mod 24)} \;=\; 5\text{ (mod 24)}


    Therefore: . 11^{30} + 5^{31} - 6 \;\equiv\;1 + 5 - 6 \text{ (mod 24)} \;\equiv\;0\text{ (mod 24)}

    The remainder is zero.
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  5. September 22nd 2012, 11:39 AM #5
    Petrus
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    Re: number theory

    ty sorban ur was clearly and i did understand :P
    maxjasper sorry u did not have alot space kinda confused me :P
    i was thinking like soo but thought it was wrong
    Last edited by skeeter; November 11th 2012 at 06:20 AM. Reason: removed expletive
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