for which value of n, 4^85+2^3373+4^n will be the perfect square ??

• given expression is in the form of a^2+2ab+b^2
  4^85=2^2(85)
  4^n=2^2n
  2^3373=2*2^85*2^n
  3373=85+1+n
  n=3373-86=3287
• 10 years agoHelpfull: Yes(64) No(6)
• (2)^170+(2)^2n+2(2^170)(2^2n)....a^2+b^2+2ab
  now compare 3373=170+2n+1
  hence n=1601
• 10 years agoHelpfull: Yes(11) No(16)
• @ramya sree. How did you just write that this equation is in the form of a2+b2
  And 2^3373=2*2^85*2^n. What made you to write this, what is the reason behind this dude.
• 9 years agoHelpfull: Yes(1) No(0)
• 4^85 + 2^3373+ 4^n
  2^(2*85) + 2^(3373)+2(2*n)
  2*85 + 3373 + 2*n must be an even number
  hence
  190 + 3373 + 2*n
  3563+2*n
  To make it even n should be equal to 1/2 or 3/2.......etc
  3563+2*1/2
  3563+1
  3564
  (2^1782)^2
• 9 years agoHelpfull: Yes(0) No(1)