What will be the remainder if(34^31)^301 is divided by 9

• (34^31)^301/9
  =[(9*3+7)^31]^301/9
  => (7^31)^301/9
  => [(7^3)^10 * 7]^301/9
  => [(9*38+1)^10 *7]^301/9
  => 7^301/9
  => [(7^3)^100 *7]/9
  => [(9*38+1)^100 *7]/9
  => 7/9 gives a remainder 7
  
  ans: 7
• 10 years agoHelpfull: Yes(41) No(2)
• (34^31)^301(a^m^n=a^mn)=(34^(31*301))=34^9331
  =>(30+4)^9331
  now we go with divisibility rule
  4^1/9=4
  4^2/9=7
  4^3/9=1
  so we have 3 choices now divide 9331 by 3 we get
  9331/3=1
  so we will take 1st possibility so ans is :4
• 10 years agoHelpfull: Yes(5) No(2)
• 32^31*107=32^3317/9
  using remainder theorem
  7^3317/9
  (-2)^3317/9
  [-{(2^3)}^1105 * 2^2 ]/9
  [-(-1)^1105 * 4 ] /9
  4/9
  So remainder 4
  
• 10 years agoHelpfull: Yes(1) No(7)
• (34^31)^301 is divided by 9 means 34^(31*301) is divided by 9
  Now 34/9 remainder is 7 So 34^(31*301) divided by 9 can be written as 7^(31*301) divided by 9 . Euler of 9 is E(9)=6 & (31*301) is divided by this E(9) that gives remainder 1.So we got 7^1 divided by 9 that means remainder is 7.
• 10 years agoHelpfull: Yes(1) No(1)
• (34^31)^301/9
  =(34^332)/9
  =((9*3+7)^332)/9
  =(7)^332/9
  =(49)^166/9
  =(4)^166/9
  =(8)^83/9
  =(-1)^83/9
  =-1/9
  =8
• 10 years agoHelpfull: Yes(1) No(6)
• can sombody plz make it more clear..@rakesh plz explain all the steps
• 10 years agoHelpfull: Yes(0) No(1)
• pls explain clearly
• 10 years agoHelpfull: Yes(0) No(1)
• right answer is = 7
• 9 years agoHelpfull: Yes(0) No(0)