Find all positive integers n which make the expression below an integer:

(25/2 + (625/4 - n)^½ )^½ + (25/2 - (625/4 - n)^½ )^½

By the way, kudos to pcbouhid for coming up with an expression that simplifies so nicely when squared.  Lots of terms cancel out.  I didn't include the math in my solution,  but the square of the expression above =

(25/2 + (625/4 - n)^½ ) + (25/2 - (625/4 - n)^½ ) +
2(25/2 + (625/4 - n)^½ )^½ (25/2 - (625/4 - n)^½ )^½   =

25 +
2(25/2 * 25/2 - (625/4 - n) )^½  =

25 + 2n^½

Posted by Steve Herman on 2009-03-21 18:04:38