WHAT IS UNIT DIGIT OF 2^(3^28439)?

• unit digit is 8.
• 10 years agoHelpfull: Yes(9) No(0)
• ans will be 8.
  28439/4=7109+3/4
  3^3=7*1(3^3=27 and 3^4=81)
  so unit place will be 7
  now 2^x.....7
  after dividing by 4
  3 will be remainder
  so 2^3=8 in unit place
• 10 years agoHelpfull: Yes(3) No(0)
• 2 as 28439 leaves remainder 3
  
• 10 years agoHelpfull: Yes(1) No(0)
• Since cyclicity of 3 is 4 (i.e. 3,9,7,1)
  so divide 28439 by 4.
  28439/4 gives remainder as 3
  That implies the unit digit for 3^28439 is 7 (check the cyclicity values).
  
  Now 2^.....7
  Since cyclicity of 2 is also 4 (i.e. 2,4,8,6)
  divide the power .....7 by 4
  
  for the power .....7 last two digits can be 07, 17, 27, 37, 47, and so on
  on dividing these numbers by 4 we either get remainder as 1 or 3
  So the answer can be both 2^1= 2 or 2^3= 8
• 9 years agoHelpfull: Yes(1) No(0)
• unit digit=8.
• 10 years agoHelpfull: Yes(0) No(0)