what is the remainder when 2^214^302 is divided by 9???

• answr shud b 4.. by the euler numbr rule
• 11 years agoHelpfull: Yes(12) No(8)
• ans is 4
  2^214^302= 2^214*302= 2^64628= 2^(6*10771+2)= 2^6*10771 *2^2=
  64^10771 *4= (9*7+1)^10771 *4
  as 9*7 is divisible by 9,so we have to consider about 1 only
  =1^10771 *4= 1*4= 4
  when 4 is divided by 9,remainder=4
  
• 11 years agoHelpfull: Yes(9) No(3)
• i am sure rem will be 7
• 10 years agoHelpfull: Yes(3) No(0)
• here 214*302=68628,
  now checking each power of 2
  (2^1)%9=2
  (2^2)%9=4
  (2^3)%9=8
  (2^4)%9=7
  (2^5)%9=5
  (2^6)%9=1
  (2^7)%9=2
  (2^8)%9=4
  so it is a cycle with element of 6.
  now
  68628%6=2
  that is 2nd element/position in remainder cycle=4,
  
  
  answer is 4
• 11 years agoHelpfull: Yes(2) No(0)
• to find the cyclicity:
  2mod9=2
  4mod9=4
  8mod9=8
  16 mod9=5
  10 mod9=1
  so cyclicity=5
  nw 214mod5=4
  4 raised to even pwr gives 6 in the unit place nw 6 mod cyclicity=6 mod5=1
  so the ans is 2 i.e the 1st rem in the cycle.
• 11 years agoHelpfull: Yes(1) No(13)
• ans=4, use negative remainder theorem.
• 11 years agoHelpfull: Yes(0) No(0)
• ans:1
  1st of sll itz 214^302 not 214*302
  as E^E=E
  So 214^302=E
  4 is modulo cycle of 2
  so 214^302 is a even no whoz last dgt is 6
  nw,
  2^E6/9
  (2^3)^E2/9
  (9-1)^E2/9
  therefore 1 is the ans
• 11 years agoHelpfull: Yes(0) No(2)