Puzzle : Can you find a number n such that, the numbers n-7, n, and n+7 have rational square roots (can be expressed as integers or fractions)? According to the book one of the solution is n =113569 /14400
This is what I have done so far:
Let p, q, r be the square roots of n-7, n, and n+7, respectively.
(n-7) * n * (n+7) = p^2 * q^2 * r^2
n^3 -49n = p^2 * q^2 * r^2
As I have 4 unknowns and only one equation, I do not know how to proceed from here. What should I do?