Find the smallest possible integer n for which (2^2-1)(3^2-1)(4^2-1).....(n^2-1) is a perfect square.With explanation please....

1) 2
2) 4
3) 8
4) 6

• 8
  
  (2^2-1)(3^2-1)(4^2-1).....(n^2-1)
  
  (2+1)(2-1)(3+1)(3-1)(4+1)(4-1)....(n-1)(n+1)
  
  = 3*1*4*2*5*3*6*5......(n-1)(n+1)
  
  = 1*2*3^2*4^2*5^2*....*(n^2)*(n+1)
  
  
  
  For minimum value of n=8 , the product is a perfect square.
• 11 years agoHelpfull: Yes(0) No(0)