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

Consider the given expression to be a function.

The domain is {x|0<=x<=156.25}
so there aren't many values to check.
f(0)=5
f(625/4)=f(156.25)=sqrt(50) = 7.071
and the function is increasing.  (Dont ask for a proof)
So we can only have f(x)=6 and f(x)=7

It turns out f(121/4)=6 and f(144)=7

so the only positive integer that yields and integer is 144.

Posted by Jer on 2009-03-20 13:22:09