Find the remainder when 25^102/ 17 and 83^261/17.Explain Plz.

1) 4 and 2
2) 4 and 3
3) 3 and 2
4) None

• 25 = 17 + 8
  (17+8)^102 /17 = 8^102/17 {by reminder theorem}
  [Actually Remainder of this : (17+8)^102 /17 = Remainder of this : 8^102/17]
  
  now 8^102/17 = 64^51/17
  which is in turn equal to (68-4)^51/17
  again by theorem it becomes (-4)^51/17
  = -4 x ( -4 )^50 /17
  = -4 x ( 16 )^25 /17
  = -4 x (17-1)^25 /17
  = -4 x -1^25 = 4
  4 is the Answer
  u can also solve by taking 25^102 = 625^51 and then (629-4)^51 and solve accordingly
  { I took 629 becoz 17 x 37 is 629 }
• 7 years agoHelpfull: Yes(0) No(0)