  Fermat's Last theorem (FLT) famously states that the equation $x^n+y^n=z^n$
has no solution in positive integers $x, y, z$ for any integer exponent $n>2$.
But does this theorem have a quantitative version? Upon initial investigation
we discovered an infinite sequence of integers $(x_n, y_n, z_n)$ with
$x_n^4+y_n^4-8=z_n^2$.
