Determine all integers $i$ such that $(i-29)(i+29)$ is a square number

Question

Determine all integers $i$ such that $$(i-29)(i+29)$$ is a square number.

I’ve tried some substitutions but none of them worked... I think that the only solutions are $i=\pm 29$, but I still don’t know how to prove it.

Answer 1

Hint: $$i^2-29^2=j^2\implies (i-j)(i+j)= 29^2$$

$$ \begin{array}{c|c} i+j & i-j & 2i& i \\ \hline 1& 29^2 & 1+29^2 &421\\ 29&29&58&29\\ 29^2&1& 1+29^2& 421\\ -1& -29^2 & -1-29^2 &-421\\ -29&-29&-58&-29\\ -29^2&-1& -1-29^2&-421 \end{array} $$