Büchi's problem

**Büchi's problem (first open case, $M = 5$)**: For all integers $x$ and $a$, if $(x+n)^2 + a$ is a perfect square for $n = 0, 1, 2, 3, 4$, then $a = 0$.

Non-trivial sequences of length 3 and 4 are known to exist, so $M = 5$ is the first open case.