Prove that for every $n \geq 6$ the equality $1/a_1^2 + ... 1/a_n^2 = 1$ has answer in $\mathbb{Z}$ (I mean it has an answer where all $a_i \in \mathbb{Z}$) (Repetition is allowed)
After some testing I found the answer $6,2,2,2,3,3$ for $n=6$ and $4,4,4,4,2,2,2$ for $n=7$. But I don't know how can I generalize this. Maybe I need to use induction but I don't know how to get from $n$ to $n+1 $ because obviously the answer completely change every time.
If it is true for $n$, then it is true for $n+3$, because $\frac{1}{a_n^2}=\frac{1}{4a_n^2}+\frac{1}{4a_n^2}+\frac{1}{4a_n^2}+\frac{1}{4a_n^2}$. So you only need to find examples for $n=6,7,8$