(3^34)/55 find out the reminder
N.B.- Here euler fails

• ans is 4
  cyclicity of 3 is 4
  s0 divide 34 by 4, u get 2 as remainder
  now 3^2 is 9
  divide 9 by 5
  remainder is 4
• 10 years agoHelpfull: Yes(19) No(13)
• According to remainder thereom
  (3^34)/55=(((3^4)^8)*3^2)/55
  ={((26)^8)*9}/55
  =(31*9)/55
  i.e.,remainder=4
• 10 years agoHelpfull: Yes(14) No(5)
• @ RITESH KUMAR and SARABESHWAR
  According to remainder thereom
  (3^34)/55=(((3^4)^8)*3^2)/55
  ={((26)^8)*9}/55
  ={[(26^2)^4]*9}/5
  ={[(16^4)*9]}/55
  =[(36^2)*9]/55
  =[(-19^2)*9]
  =(361*9)/55
  =[{(55*6)+31}*9]/55
  =(31*9)/55
  i.e.,remainder=4
  
• 10 years agoHelpfull: Yes(9) No(5)
• Ans is 4
  (a*b*c)%x=a%x*b%x*c/x.
  (3^34)%55=(3^10%55)*(3^10%55)*(3^10%55)*(3^4%55)
  3^10%55=(3^4%55)*(3^4%55)*3^2%55
  so 3^10%55=26*26*9%55=34
  so then
  3^34=34*34*34*26=4
• 10 years agoHelpfull: Yes(7) No(1)
• Kv Chowdary friend how come you got 31 plzzz explain
• 10 years agoHelpfull: Yes(1) No(1)
• first -55=5*11
  then apply euler
• 10 years agoHelpfull: Yes(1) No(0)
• (3^34)/55 can also be written as (9^17)/55
  now apply binomials theorem and the result will become 169/55 whose remainder is 4
• 10 years agoHelpfull: Yes(1) No(0)
• (3^34)/55=(((3^4)^8)*3^2)/55
  ={((26)^8)*9}/55
  ={[(26^2)^4]*9}/5
  ={[(16^4)*9]}/55
  =[(36^2)*9]/55
  =(31*9)/55
  =279/55
  =4
• 10 years agoHelpfull: Yes(1) No(0)
• any no. can be written in form 4n+1 ...3^34 =3^(32+2)=3^2=9
  9/55 remainder = 9
• 10 years agoHelpfull: Yes(0) No(0)
• Remainder is 4
• 10 years agoHelpfull: Yes(0) No(1)
• 3^34/55=3^2/(5^1*11^1)=9/5=4
  for finding reminder of a number
  for base we have to take the unit digit and for power we have to divide with 4
  ex:31^22=(1)^2=1 is unit digit
• 10 years agoHelpfull: Yes(0) No(0)
• @ KV CHOWDARY 3^4 that becames 26.....how
• 10 years agoHelpfull: Yes(0) No(0)
• According to remainder thereom
  (3^34)/55=(((3^4)^8)*3^2)/55
  ={((26)^8)*9}/55
  ={[(26^2)^4]*9}/5
  ={[(16^4)*9]}/55
  =[(36^2)*9]/55
  =[(-19^2)*9]
  =(361*9)/55
  =[{(55*6)+31}*9]/55
  =(31*9)/55
  i.e.,remainder=4
• 10 years agoHelpfull: Yes(0) No(2)