what is the remainder of (16937^30)/31 ?

• (16937^30)/31
  = ((16937%31)^30)%31 i.e (11^30)%31 (by remainder theorem)
  = (121^15)%31
  =(28^15)%31 =28(784^7)%31
  =28(9^7)%31
  =28*9*(19^3)%31
  =1728468%31=1
  
• 10 years agoHelpfull: Yes(28) No(1)
• @ JIGNESHKORADIYA
  1 is the ans
  (16937^30)/31=(15^30)/31(as 15 is the remainder when 16937 is divided by 31)
  we can write (15^30)/31 as (225^15)/31
  which is equal to (8^15)/31 (as 8 is the remainder when when 225 is divided by 31)
  we can write 8^15/31 as (64^7*8/31) = (2^7*8/31) as 2 is remainder when 64 is divided by 31
  we can write 2^7*8/31 as ((32*2^2)*8)/31 =(32*32)/31
  which when divided by 31 leaves remainder (1*1)/31
  so remainder is 1
• 10 years agoHelpfull: Yes(9) No(11)
• 1 is the answer
• 10 years agoHelpfull: Yes(6) No(1)
• answer is 1.consider last two digits 37^30/31= 7^30. odd power even is 1
• 10 years agoHelpfull: Yes(3) No(0)
• by using fermats theorem u can directly get the ans 1.
  
• 10 years agoHelpfull: Yes(3) No(0)
• ravi kumar,will u pls tell me what is fermest theorem??
• 10 years agoHelpfull: Yes(3) No(0)
• when we divide 16937 by 31 we got 15 as remainder
  then we have now (15)^30 so make (15*15) groups of this will result in 15 group
  now divide 225/31 we got remainder 8 of 15 times so make (8*8) groups this will result in 7 groups and one 8 extra
  now divide 64%31=2
  this 2^7 and 2^3= 2^10%31 we got final result 1
• 10 years agoHelpfull: Yes(2) No(5)
• 16937%31=11
  11^30=11^28*11^2
  11^2=121%31=28
  hence ans=28 % =remainder
• 10 years agoHelpfull: Yes(2) No(2)
• ans is 1
  [sakshi sahni]
  (16937^30)/31
  = ((16937%31)^30)%31 i.e (11^30)%31 (by remainder theorem)
  = (121^15)%31
  =(28^15)%31 =28(784^7)%31
  =28(9^7)%31
  =28*9*(19^3)%31
  = 252%31 * 19^2%31
  =14*20%31
  =so remainder is 1
• 9 years agoHelpfull: Yes(2) No(0)
• i think 30 is the answer to the question
• 10 years agoHelpfull: Yes(1) No(3)
• plz explian any oneeeeeeee
• 10 years agoHelpfull: Yes(1) No(0)
• 1 is the answer
  
• 10 years agoHelpfull: Yes(1) No(0)
• using remainder theorem ans is 1
• 10 years agoHelpfull: Yes(1) No(0)
• Here on Dividing 16937 by 31 we get 15 ramainder
  thus now we can write
  ((15)^30)/(31)
  
  Now taking 15*15 we can write
  ((225)^15)/(31)
  
  on Dividing 225 by 31 we get 8 as remainder
  so we can write
  ((8)^15)/(31)
  
  Taking 8*8
  ((64)^7*8)/(31)
  
  64%31 is 2
  so
  (2^7*8)/(31)
  
  taking 2^5=32 we can write
  (2^5*4*8)/(31)
  
  32%31 is 1
  so we are left with
  (1*4*8)/(31)
  thus it is 32%31=1
  so 1 is answer
• 9 years agoHelpfull: Yes(1) No(1)
• no not 30 its 24......
• 10 years agoHelpfull: Yes(0) No(3)
• 11 is the ans
• 10 years agoHelpfull: Yes(0) No(1)
• 1 will be the remainder !!!
• 10 years agoHelpfull: Yes(0) No(0)
• use the fermet theorem a^p-1/p =1 where p is a prime number
• 9 years agoHelpfull: Yes(0) No(0)
• Euler thereom says:
  a^(p-1)/ p = 1 remainder
  where p - prime number
  a - natural number
  
  In this question 31 is a prime number
  So a^30/31 = 1 remainder
• 6 years agoHelpfull: Yes(0) No(0)