Is there a simple proof that if $(b-a)(b+a) = ab - 1$, then $a, b$ must be Fibonacci numbers?
104807
Prove the inequality $\left|\frac{m}{n}-\frac{1+\sqrt{5}}{2}\right|<\frac{1}{mn}$
60712
Induction Proof: Fibonacci Numbers Identity with Sum of Two Squares
131400
Solution check: Let $f_n$ be fibonacci numbers. Prove: $\sum_{k=0}^{n-1} \binom{n+k}{2k+1} = f_{2n-1}$ and $\sum_{k=0}^n \binom{n+k}{2k} = f_{2n}$
91068
Proving that $f_2+f_4+\cdots+f_{2n}=f_{2n+1}-1$ for Fibonacci numbers by induction
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
139934
In $\mathbb{Z}/(n)$, does $(a) = (b)$ imply that $a$ and $b$ are associates?
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
57416
Fibonacci identity: $f_{n-1}f_{n+1} - f_{n}^2 = (-1)^n$
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
96027
Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite.
89175
Proof of $(a+b)^{n+1}$
925
Prove that $F_n={n-1 \choose 0 }+{n-2 \choose 1 }+{n-3 \choose 2 }+\ldots$ where $F(n)$ is the $n$-th fibonacci number
106981
Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$
65466
How to prove this Fibonacci sequence statement: $F^2_{n+1} - F^2_{n-1} = F_{2n}$
42105
Fibonacci proof by induction
127848
Determine which Fibonacci numbers are even