Find all integers n for which √(25/2 + √(625/4 –n)) + √(25/2 - √(625/4 –n)) is an integer.

(In reply to re(3): solution & playing around by Charlie)

Surprising, because:

4k^4+8k^3-44k^2-48k+144 = 4(k-2)^2(k+3)^2
(2*p^2 + 10p)^2 = 4p^2(p+5)^2

Let k=(p+2), then the formulae look very much the same.

Posted by broll on 2015-03-10 22:49:35