Find the remainder when 128 ^1000 is divided by 153?

• 128^1000/153 = 128^1000/17.9
  
  now when 128^1000 is divided by 17 rem
  
  2^7000/17 = 16^1750/17 = (17-1)^1750/17 so rem = 1
  
  it can be represented by 17a +1.............(1)
  
  when 128^1000 is divided by 9
  
  2(3*333 + 1)mod9 = -1*2mod9 = 7mod9 so rem = -1.2 = -2 = 7
  
  it can be represented by 9b + 7............(2)
  
  equating (1) and (2)
  
  17a+1=9b+7 => 9(b-a) = 8a - 6
  this is true for a = 3
  
  so remainder = 17*3 +1 = 52
• 11 years agoHelpfull: Yes(8) No(2)
• is it 0 ???
• 11 years agoHelpfull: Yes(3) No(3)
• 60
  break 153 into 9 and 17 and den divide to find remaider..
  
• 11 years agoHelpfull: Yes(1) No(19)
• It is 52 !!!
• 11 years agoHelpfull: Yes(1) No(1)