How many real solutions does the equation ⌊x²⌋ = (x - ¹⁄₅₀)² have? How many are rational?

For every non-negative integer N,
x = (√N) + 1/50 is a real solution.
When N is a perfect square, it is a rational solution.
So, an infinite set of real and an infinite set of rational solutions.

I am suspicious that there may be more solutions, but I haven't seen it yet.

Posted by Larry on 2023-04-03 08:36:55