query: How to find reminder of $m^{x}$ divided by $n$ using Euler's and Fermat's little theorem
positive_passages.docid: 360
positive_passages.text: Modular exponentiation by hand ($a^b\bmod c$)
negative_passages.docid: 19500
negative_passages.text: How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?
negative_passages.docid: 91914
negative_passages.text: Prove that for the Fibonacci sequence $(F_n)$, $F_n$ divides $F_{2n}$.
negative_passages.docid: 75166
negative_passages.text: Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$
negative_passages.docid: 52353
negative_passages.text: Bounding Euler's e by showing $2 \leq \left (1+ \frac{1}{n}\right)^n < 3$
negative_passages.docid: 109576
negative_passages.text: Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$
negative_passages.docid: 133181
negative_passages.text: Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
negative_passages.docid: 17690
negative_passages.text: Ways to prove Euler's formula for $\zeta(2n)$
negative_passages.docid: 95653
negative_passages.text: Euler's theorem: [3]^2014^2014 mod 98
negative_passages.docid: 48655
negative_passages.text: Find all n such that : $3 \mid (n2^{n}+1)$
negative_passages.docid: 130223
negative_passages.text: Proving a special case of the binomial theorem: $\sum^{k}_{m=0}\binom{k}{m} = 2^k$
negative_passages.docid: 16697
negative_passages.text: Fermat Last Theorem for non Integer Exponents
negative_passages.docid: 151636
negative_passages.text: Fast way to calculate n! mod m where m is prime?
negative_passages.docid: 144017
negative_passages.text: How to find the smallest $n$ such that $n^a\equiv 1 \pmod p$
negative_passages.docid: 49938
negative_passages.text: Proof of $a^{\phi (n) +1} \equiv a \pmod{\! n} $ Carmichael generalization of Fermat-Euler's theorem.
negative_passages.docid: 51653
negative_passages.text: Prove that $m+\frac{4}{m^2}\geq3$ for every $m > 0$
negative_passages.docid: 8884
negative_passages.text: Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$