For $f_n^2 - f_{n-2}^2 = f_{2n-1}$
132089
How do I prove/disprove that $F_n^2 + F_{n\pm 1}^2 = F_{2n\pm 1}$, where $F_n$ is the $n$th Fibonacci number?
124131
Show that $(x-1)^2$ is a factor of $x^n -nx +n-1$
9920
$(n^2 - 1)!$ is a multiple of $(n!)^n$
75863
how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
83080
Question regarding $f(n)=\cot^2\left(\frac\pi n\right)+\cot^2\left(\frac{2\pi}n\right)+\cdots+\cot^2\left(\frac{(n-1)\pi}n\right)$
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
12910
For the Fibonacci numbers, show for all $n$: $F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
31698
$f(m^2 + f(n)) = f(m)^2 + n$ for all natural numbers
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
76610
Show that $f^{-1}(A \cup B) = f^{-1}(A) \cup f^{-1}(B)$
62254
Show $F_{n+1} \cdot F_{n-1} = F_n^2 + (-1)^n$ for all $n \in \mathbb{N}$
10024
How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)
60348
How do I prove $F(a)=F(a^2)?$
50655
Proof of $f^{-1}(B_{1}\setminus B_{2}) = f^{-1}(B_{1})\setminus f^{-1}(B_{2})$
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
65923
How to approach proving $f^{-1}(B\setminus C)=A\setminus f^{-1}(C)$?