What is the remainder of (222)^222 / (16)^15

• zero
  (222)^222 / (16)^15 = (2^222 *111^222)/(2^60) = (2^162)*(111^222)
  
  zero remainder
• 12 years agoHelpfull: Yes(27) No(0)
• @ Kartheek Goli,
  
  Why r u taking mod 7 ?
  
  I think u hv pasted the solution of some other question by mistake.
  Pls check.
• 12 years agoHelpfull: Yes(5) No(0)
• (222)^222=(111*2)^222
  (16)^15=(2*2*2*2)^15=2^60
  (111*2)^222/2^60=(111)^60*(222)^162 so remainder 0
• 12 years agoHelpfull: Yes(2) No(1)
• 222^222 mod 7
  
  (31*7+5)^222 mod 7
  
  5^222 mod 7
  
  (25)^111 mod 7
  
  
  (7*3+4)^111 mod 7
  
  (4)^111 mod 7
  
  (16)^55.(4)^1 mod 7
  
  (7*2+2)^55.4 mod 7
  
  (2)^55.4 mod 7
  
  (8)^18.8 mod 7
  
  (7+1)^18.8 m0d 7
  
  (1)^18.8 mod 7
  
  1*8 mod 7=1
  
  1 (ans)
• 12 years agoHelpfull: Yes(1) No(13)