Remainder when 50^56^52 divided by 11

• 50^56^52 mod 11
  56^52 mod 10
  6^52 mod 10
  -
  10=2*5
  6^52 mod 2=0
  6^52 mod 5=1
  2a=5b+1
  remainder= 6
  -
  50^6 mod 11
  6^6 mod 11
  36^3 mod 11
  27 mod 11 = 5 ans
• 10 years agoHelpfull: Yes(22) No(9)
• ans:3
  sol:50^56^52=50^2912
  Rem=50^2912/11=>(5*10)^2912/11
  =>5^2912*10^2912/11
  =>3*1/11=3(rem) [since 5^2912 leaves rem 3 and 10^2912 leaves a rem 1 ]
• 10 years agoHelpfull: Yes(10) No(9)
• 50^56^52=(44+6)^56^52
  just take the following
  =6^56
  =36^28
  =(33+3)^28
  =3^4*7
  =81^7
  =(77+4)^7
  4^7
  
  having reminder 5
  am i ri8
• 10 years agoHelpfull: Yes(9) No(5)
• ans=
  (55-5)^56^52/11
  =5^56^52/11
  =5^2912/11
  =5/11
  =5 remainder
• 10 years agoHelpfull: Yes(7) No(3)
• THE ans IS 4
  USE REMAINDER THEOREM DIRECTLY OR NEGATIVE REMAINDER THEOREM MAKES IT FURTHUR EASY
  SIMPLE ONE
  50*56*52/11 -R->(6)(1)(8)/11=48/11====4 ANS
  NEGATIVE REMAINDER
  (-5)(1)(-3)/11==15/11===4 ANS
• 10 years agoHelpfull: Yes(7) No(6)
• 50^56^52/11=50^(55+1)^52/11
  =50^1^52/11=50^1/11=50/11=6ans
  
• 10 years agoHelpfull: Yes(5) No(13)
• we can write 56^52 as (55+1)^52
  here 55 is divisible by 11 but the problem is 1 so
  1^52 = 1 therefore
  any power of 50 will end with 1 as 50^...................1
  now we can write 50^...1 as (44+6)^...1 here 44 is divisible by 11 and the remaining part is 6^.....1
  now if u see
  6^1=6
  6^2=36
  6^3=216
  6^4=1296
  here any power of 6 is ending with 6
  so the unit digit of 6^.....1 will also be 6 and all the numbers is divisible by 11 and 6 is remain as extra which is not further divisible so the remainder is 6
• 10 years agoHelpfull: Yes(3) No(6)
• 50/11=6
  now, euler of 11 is 10.thus dividing power of 50 by 10 we get 6 as remainder
  thus 6^6/11=6 . 6 is the ans.
• 9 years agoHelpfull: Yes(2) No(2)
• REM (50*56*52/11)= Rem ((44+6)(55+1)(44+8)/11) =Rem (6*!*8/11)=4
• 10 years agoHelpfull: Yes(1) No(7)
• 3
  [50^56^52/11]=[6^(56*52)/11]=[6^2842/11]
  as 11 is prime and 6,11 are co prime. [6^10n/11]=1
  so
  [6^2/11] matters
  or [36/11]=3
• 10 years agoHelpfull: Yes(0) No(8)
• Ans is 3.
  50 to the power anything will result in the end digits of ...250000...... .
  Now, if no of 0s are even, then the rem will always be 3.
  Clearly, 56^52 is even no., thus the ans is 3.
• 10 years agoHelpfull: Yes(0) No(3)
• answer is 1.
  {(50)^56^52}/11={(6)^56^52}/11={(6^4)14^52}/11={(-1)14^52}/11=1/11=1
  thus remainder is 1.
• 10 years agoHelpfull: Yes(0) No(3)
• Ans is 6.
  where phi(11)=(1-1/11)*11=10
  => So 51^52 is to be written in the form of 10k + a.
  Now unit digit of 56^52 = 6 => 56^52 = 10k + 6.
  => 50^56^52 = 5010k + 6 = 506mod11 = 6
  
• 10 years agoHelpfull: Yes(0) No(4)
• 50^56^52 /11 = remainder 3 .
• 9 years agoHelpfull: Yes(0) No(4)
• 5 is the correct answer.
  
• 7 years agoHelpfull: Yes(0) No(0)
• 5652 = 10k + 6
  => 5010k + 6 = 506mod11 = 56mod11 = 5mod11
• 7 years agoHelpfull: Yes(0) No(0)
• We need to find out Rem [50^56^52 / 11] = Rem [6^56^52 /11]
  
  Now, by Fermat's theorem, which states Rem [a^(p-1)/p] = 1, we know
  Rem [6^10 /11] = 1
  => Rem [6^10k / 11] = 1
  
  The number given to us is 6^56^52
  Let us find out Rem[Power / Cyclicity] t0 find out if it 6^(10k +1) or 6^(10k +2). We can just look at it and say that it is not 6^10k
  
  Rem [56^52 / 10] = 6
  => The number is of the format 6^(10k + 6)
  
  Now, we need to calculate Rem [6^56^52 /11]
  = Rem [ 6^(10k + 6) / 11]
  = Rem [6^6*6^10k / 11]
  = Rem[216^2/11] * Rem [6^10k / 11]
  = Rem [7^2/11] * 1
  
  = Rem [49/11]
  
  = 5
• 6 years agoHelpfull: Yes(0) No(0)