anonymous
  • anonymous
What's the reminder when 2^34 is divided by 5? plz help
Mathematics
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SOLVED
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chestercat
  • chestercat
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Isaiah.Feynman
  • Isaiah.Feynman
2^34 is a very large number, when you divide it by 5 you have no remainder.
AkashdeepDeb
  • AkashdeepDeb
I am not sure of any direct way to do this but yeah there is a logical way! We OBVIOUSLY will not calculate the 2^34 value :P So what we do is we find out what are the remainders at each stage and find a pattern! Like this.... 2^1 leaves remainder --- 2 --- when divided by 5 2^2 leaves remainder --- 4----when divided by 5 2^3 leaves remainder --- 3--- when divided by 5 2^4 leaves remainder --- 1----when divided by 5 2^5 leaves remainder --- 2 --- when divided by 5 2^6 leaves remainder --- 4----when divided by 5 And it goes on so we see that! The pattern of remainder is 2,4,3,1,2,4,3,1..... All we have to do is see which one corresponds to 34!! :) Understood? :)
anonymous
  • anonymous
31

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zzr0ck3r
  • zzr0ck3r
so 2 has order 4 mod(5)
AkashdeepDeb
  • AkashdeepDeb
@Isaiah.Feynman Try it out with a calc! It does have a remainder! :)
anonymous
  • anonymous
4 i think
Isaiah.Feynman
  • Isaiah.Feynman
Looks like my its beyond my calculator. lol
AkashdeepDeb
  • AkashdeepDeb
XD
anonymous
  • anonymous
3+1
zzr0ck3r
  • zzr0ck3r
2^{34} conruent 2^6 congruent to 4 mod(5)
AkashdeepDeb
  • AkashdeepDeb
Exactly so it should be! 4 !! :D Because 2^36 remainder is 1 [Because 36 is a multiple of 4] And so 2^35 would be 3 And so 2^34 would be 4!! Check the pattern @CoolJolie
anonymous
  • anonymous
how ur saying 2^36 is four@AkashdeepDeb
anonymous
  • anonymous
sorry 1
AkashdeepDeb
  • AkashdeepDeb
Because 2^36 has a degree of 36 and we know that 36 is a multiple of 4! And we saw that 2^4 had a remainder of 1 too!! :) And so did 2^8 = 256 has a remainder of 1 :D Got it? :) And so we trace the pattern backwards and we get 2^34 as 4 :D
anonymous
  • anonymous
yes ur right
AkashdeepDeb
  • AkashdeepDeb
:)
anonymous
  • anonymous
i thought 2^3=3 2^4=1 so 3+1=4 and
AkashdeepDeb
  • AkashdeepDeb
Haha. No! That is a funny way though! : ' )
anonymous
  • anonymous
but 2^36= 3+4=7 2^7=1
anonymous
  • anonymous
bcoz 2^4 leaves 1 when divided by 5 hence 2^32=(2^4)^8 will leave remainder 1 when divided by 5 hence 2^34=2^2 * 2^32 so when 2^34 is divided by 5 remainder is 4

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