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

(In reply to re: Simplifying matters (Spoiler) (some thoughts) by Daniel)

Daniel:

I haven't gone through all your math, but I suspect that you went wrong at the next-to-last step.

Your expression, (25+2sqrt(n))/2

is exactly half of mine (  25 +2n½  ).

I notice that you seem to have added 25/2 + 25/2 and come up with 25/2, when the correct sum is 25.  Probably the same halving occurred with the square roots.

Steve

Posted by Steve Herman on 2009-03-25 11:05:03