2^46655 mod 9 = ?

• if there is given 2 to the power something, then we can simply use 2^unit digit of that power.. so we get- 2^46655mod9= 2^5/9=5 ans
• 9 years agoHelpfull: Yes(33) No(1)
• By remainder theorem
  Remainder={[(2^3)^1551*2^2]/9}
  =[{(-1)^1551*4}/9]
  =5
• 9 years agoHelpfull: Yes(25) No(3)
• 2^46655=(2^3)^15521*2^2=-4=5
• 9 years agoHelpfull: Yes(4) No(1)
• (2^4)^11663+(2)^3
  =(....6)^11663+8
  =(......6)+8
  last 2 digit=8+6=14
  therefore 14 mod 9=5
• 9 years agoHelpfull: Yes(4) No(0)
• (2^5)^9331 %9
  =5^9331%9
  this 5 will recur
• 9 years agoHelpfull: Yes(4) No(0)
• 2^46655 mod 9
  2^5=2
  2mod 9=2
• 9 years agoHelpfull: Yes(2) No(8)
• Answer will be 2^5 mod 9 = 32 mod 9= 5
• 9 years agoHelpfull: Yes(2) No(1)
• if any 1 knows euler totient theorem..this is the best method
  [ eulers totient theorem
  
  N^totient(X) mod X = 1
  ]
  
  totient no. of 9 = totient(9) =6
  
  dividing 46655 by 6 leaves remainder = 5
  
  therefore equation reduces to 2^5 mod 9 = 5
• 9 years agoHelpfull: Yes(1) No(0)
• divide this in (2^3)^46653*2^2/9
  then (2^3)^46653/9 will give you remainder -1 as the power of 2 is negative
  and 2^2 will give you 4
  thn -1*4=-4
  that will give you 9-4=5 (as negative remainder)
• 9 years agoHelpfull: Yes(1) No(0)
• 2 mod 9 = 2
  46655 mod 8=7
  2^7 mod 9=2
  2 is ans
• 9 years agoHelpfull: Yes(0) No(6)
• ans is 5
  remainder will be 5
• 9 years agoHelpfull: Yes(0) No(2)
• ans is 5
  4*(8)^1551/9
  =4(-1)/9
  =-4 i.e.,9-4=5 is rem
• 9 years agoHelpfull: Yes(0) No(0)
• let me explain plz smita paul how u get(..6)^11663=6.plz
• 9 years agoHelpfull: Yes(0) No(0)
• use euler formula for this as 2 and 9 are coprime.totient function is equal to 6 as 9=3^2 so it is equal to 9*(1-1/3)=6 so 2^6 mod 9=1.46655 have a unit digit 5 so we can reduce the whole 2^46655 number into 2^(6*k+5)/9 . 32mod 9 is equal to 5.
• 9 years agoHelpfull: Yes(0) No(1)
• (2^3)1551*2^2
  for formula a^n/(a+1)=a if n is odd and 1 if n is even
  so 1551 is odd so the new expression is
  8*2^2/9=32mmod9=5
• 9 years agoHelpfull: Yes(0) No(0)
• (2^46655)%9=(((2^6)^7775)*(2^5))%9 ===> (2^5)%9 == 32%9= 5
  so (2^46655)%9= 5
  {since for (2^x)%9 the remainders repeat for every 6 powers of 2}
• 9 years agoHelpfull: Yes(0) No(0)