When 31^31^301 divided by 9 what is the remainder?

• [31^31^301] % 9 .............. here % operator stands for reminder after divide
  = [(3*9 +4)^31^301] % 9
  = [4^31^301] %9
  
  Now, 4^3 = 64 = 9*7 + 1
  hence we first should find reminder of 31^301 when divided by 3
  
  [31^301] % 3
  = [(3*10 + 1) ^ 301] % 3
  = [1^301] % 3
  = 1
  therefor we can conclude
  [31^301] = 3*integer + 1 = 3i+1 (say)
  
  
  hence
  [31^31^301] % 9
  = [4^31^301] %9
  = [4^(3i+1)] % 9
  = [4*(4^3i)] % 9
  =[4*(64^i)]%9
  =[4*{9*7 + 1}^i] % 9
  = [4*{1}^i] % 9
  =[4] % 9
  = 4
  
  hence reminder = 4
  
  enjoy
• 9 years agoHelpfull: Yes(0) No(0)