FIND THE REMAINDER WHEN 25^102 IS DIVIDED BY 17.

• 25^102/17=8^102/17(Remainder of 8/17=25/7).
  ((2^3)^102)/17=2^306/17=(2^2*(2^4)76)/17
  =4*(16)^76/17
  =4*(-1)^76/17
  =4/17
  Remainder is 4
• 11 years agoHelpfull: Yes(23) No(3)
• remainder is 1 see how (17+8)^102/17 after that (8)^102/17= (8)^2^51/17 i.e (64)^51/17=(63+1)^51/17 after that (1)^51/51 therefore remainder is 1
  answer remainder is 1.
• 11 years agoHelpfull: Yes(13) No(22)
• 25^102/17
  =(17+8)^102/17 = 8^102/17 = (4+4)^102/17 = [4^102 + 4^102]/17
  =16^51/17 + 16^51/17 = (17-1)^51/17 + (17-1)^51/17 = -1-1.
  
  so, remainder will be -2.
• 11 years agoHelpfull: Yes(5) No(18)
• 25^102=(25^3)^34=(15625)^34
  15625/17 remainder = 2
  2^34/17
  2^34= 4*(2^4)^8/17=4*(16)^8/17
  =4*(-1)^8/17=4/17
  remainder = 4
• 11 years agoHelpfull: Yes(5) No(2)
• 4
  25^102=25^6=625*625*625
  rem when 625/17=13
  13*13*13/17
  the rem is=4
• 11 years agoHelpfull: Yes(3) No(4)
• 
  
  rem 8
  
  just check for the once and tens place at every iteration of power of 25
  I.e.
  25^1=25
  25^2=625
  .
  .
  25^6=244140625
  every step we can see that 25 repeats itself for the last two digits(i.e. once and tens position) now divide the last two digit by the divisor
  25/17 and we get remainder as 8.
  
  Remainder= 8
• 11 years agoHelpfull: Yes(2) No(3)
• 2 is correct answer..............
  bcoz the logic is ......../
  according to fermats rule we can do it .....ie.if GCD(a,p)=1,then a^(p-1)=1mod(p).
  so now GCD(25,17)=1 so no aply the formula 25^(17-1)=1mod(17)....it will give remainder= 2
  if anybody more clarity mail me....if u like my ans...then clik on yes....
• 11 years agoHelpfull: Yes(1) No(2)
• as by euler law as 17 is prime
  so 25^16/17=1 now we have
  remainder of 25^101/17=remainder of 25^(16*6)*25^5/17
  remainder of 25^5/17=reminder of 8^5/17=64*64*8/17
  remainder of 13*13*8/17=9
  so ans is 9
  
• 11 years agoHelpfull: Yes(0) No(2)
• (x^n +1) will be divisible by (x+1) if n is odd.
  so,(67^67 +1) will be divisible by (67+1) cz n is odd.
  so, (67^67 +67)=(67^67 +1)+66 ,when divided by 68 will give 66 as reminder.
• 11 years agoHelpfull: Yes(0) No(2)
• 25^102=(25^2)^51=(625^3)^17. so remainder is=0.
• 11 years agoHelpfull: Yes(0) No(2)
• remainder=10
  
• 11 years agoHelpfull: Yes(0) No(0)
• remainder is 4
  
• 11 years agoHelpfull: Yes(0) No(0)
• Please anybody tell me what the ^ means????
• 11 years agoHelpfull: Yes(0) No(0)
• correct ans :5
  
  5/17=5
• 10 years agoHelpfull: Yes(0) No(0)