6^50/215 Find remainder

• 6^50 mod 215
  (6^3)^16 * 6^2 mod 215
  216^16 * 36 mod 215
  [216^16 mod 215] * [6 mod 215]
  [(215*1 + 1)^16 mod 215] * [6 mod 215]
  (1^16 mod 215) * (6 mod 215)
  (1 * 36) mod 215
  36 mod 215
  
  Ans : 36
  
• 10 years agoHelpfull: Yes(13) No(1)
• [(6^3)^16]*6^2 = 6^50
  first part when devide by 215 gives 1 remainder because 6^3=216
  then overall remainder=36
• 10 years agoHelpfull: Yes(2) No(0)
• (6^3)^16*6^2/215
  (216)^16*6^2/215
  (-1)^16*36
  (-36)
  215-36=179
  
• 10 years agoHelpfull: Yes(1) No(6)
• 6^50= ((5+1)^49 * 6)/(5*43)
  so rem will be 6
  coz {(5+1)^49}%5 = 1
  
  
• 10 years agoHelpfull: Yes(1) No(3)
• (6^3)^16*6^2/215
  (216)^16*6^2/215
  (-1)^16*36
  1*36=36
  
• 10 years agoHelpfull: Yes(1) No(0)
• Remainder theorem
  {[(6^3)^16]*6^2}/215 = 6^50/215
  =(-1^16)*36/215
  =36/215
• 10 years agoHelpfull: Yes(1) No(0)
• 6^1/215=6,6^2/215=36,6^3/215=1,cycle of 3
  50/3=2
  ans=36
• 10 years agoHelpfull: Yes(0) No(0)