what is the remainder when 128^1000 is divided by 153.

• 128^1000/153
  =(16384)^500/153
  =(153*107+13)^500/153
  =13^500/153
  =169^250/153
  =(153+16)^250/153
  =16^250/153
  =(4096^83)*16/153
  =(153*27-35)^83*16/153
  =(-35)^83*16/153
  =(1225)^41*16*(-35)/153
  =(153*8+1)^41*16*(-35+153)/153
  =16*118/153=1888/153 gives remainder 52
  ans 52
• 10 years agoHelpfull: Yes(22) No(1)
• 128^1000/153
  =128^1000/9*17
  now 128^1000/9=2^7000/9=(2^3)^2333*2/9=(9-1)^2333*2/9=(-1)^2333*2/9=-2/9 gives ramainder 7 so canbe written as 9x+7
  and 128^1000/17=(2^4)^1750/17=(17-1)^1750/17 gives remainder 1 so canbe written as 17y+1
  solve 9x+7=17y+1, for least +ve integral value of x or y
  or 9(x-y)=8y-6
  or y=3,x=5
  hence remainder is 9x+7=9*5+7=52
  0r 17y+1=17*3+1=52
  ANS 52
• 10 years agoHelpfull: Yes(12) No(0)
• ans: 52
  128^2/153 gives remainder 13
  13^2 gives remainder 16
  16^2 gives remainder 103
  103^2 gives 52
  so going on
  103^2/153
  remainder 52
• 10 years agoHelpfull: Yes(4) No(0)
• Remainder will be 52
  It can be solved by remainder theorem
• 10 years agoHelpfull: Yes(4) No(0)
• explain it
• 10 years agoHelpfull: Yes(2) No(0)
• I have done this in a slightly crude method.I will try to find a more refined method.
  
  (2^7)^1000 is 2^7000 = (2^5)^1400
  
  When powers of 32 are divided by 155, it will follow a cycle of 32, 94, 63 and 1.
  The cyclicity is 4.
  
  S0,(32)^1400 is ((32)^4)^350 so the remainder is (1)^350
  
  The remainder is 1
  
  
• 10 years agoHelpfull: Yes(2) No(5)
• bhaiyo aur deviyo ans. is 52..........
  bhavnao me beh gya tha..
  
• 10 years agoHelpfull: Yes(2) No(0)
• 128^2%153 gives remainder 13
  13^2%153 gives remainder 16
  16^2%153 gives remainder 103
  103^2%153 gives remainder 52
  52^2%153 gives remainder 103(here cycle repeats)
  so remainder is 52...
  128^2%153 gives remainder 13
  128^2%153 gives remainder 13
• 10 years agoHelpfull: Yes(1) No(2)
• what`s the right answer?
• 10 years agoHelpfull: Yes(0) No(0)
• what is remainder theorm
• 10 years agoHelpfull: Yes(0) No(0)
• Ans. is 103
  rok ske to rok lo
• 10 years agoHelpfull: Yes(0) No(2)
• i think d answer is 16.
  
• 10 years agoHelpfull: Yes(0) No(2)
• Answer will be 128
  
  because,
  rem = 128-153 = -25
  but rem can not be -ve so
  rem = [ 153 - 25 ] = 128( final ans)
• 1 year agoHelpfull: Yes(0) No(0)