In a proof by induction why $\sum_{i=0}^n f^2_i = f_nf_{n+1}$ for $n\in \mathbb N$ the base case from the solution is $f_1^2=f_1f_2=1$. I assume $f$ denotes a function, but from the exercise there is no information given what $f$ denotes. So why is $f_1^2=f_1f_2=1$?
The exercise is the seventh from this sheet if additional information is needed.
The last line of the inductive step mentions the recurrence relation defining the $f$-numbers - namely that $f_{k+2} = f_{k} + k_{k+1}$ and that gives it away: $f_n$ denotes the $n$th Fibonacci number.