query: Quadratic Residue of Fibonacci numbers
positive_passages.docid: 20158
positive_passages.text: Conjecture regarding Pisano period of prime numbers
negative_passages.docid: 40156
negative_passages.text: Determine all primes $p$ for which $5$ is a quadratic residue modulo $p$
negative_passages.docid: 157601
negative_passages.text: Proof a formula of the Fibonacci sequence with induction
negative_passages.docid: 145105
negative_passages.text: What is the sum of all the Fibonacci numbers from 1 to infinity.
negative_passages.docid: 8336
negative_passages.text: How are we able to calculate specific numbers in the Fibonacci Sequence?
negative_passages.docid: 127848
negative_passages.text: Determine which Fibonacci numbers are even
negative_passages.docid: 27217
negative_passages.text: For the Fibonacci sequence prove that $\sum_{i=1}^n F_i= F_{n+2} - 1$
negative_passages.docid: 121128
negative_passages.text: Calculating a Residue at one of the poles of $\frac{1}{1+z^n}$
negative_passages.docid: 106183
negative_passages.text: Proof by Induction: Alternating Sum of Fibonacci Numbers
negative_passages.docid: 130162
negative_passages.text: A complete residue system from an arithmetic progression
negative_passages.docid: 116778
negative_passages.text: Calculation of an integral via residue.
negative_passages.docid: 7003
negative_passages.text: Inductive proof of a formula for Fibonacci numbers
negative_passages.docid: 27968
negative_passages.text: Fibonacci sequence proof
negative_passages.docid: 29979
negative_passages.text: When is $-3$ a quadratic residue mod $p$?
negative_passages.docid: 42435
negative_passages.text: Proof of this result related to Fibonacci numbers: $\begin{pmatrix}1&1\\1&0\end{pmatrix}^n=\begin{pmatrix}F_{n+1}&F_n\\F_n&F_{n-1}\end{pmatrix}$?
negative_passages.docid: 108872
negative_passages.text: Residues of $z^2\sin(\frac{1}{z})$
negative_passages.docid: 80754
negative_passages.text: A slight modification in Chinese Remainder Theorem