query: Prove $p\mid\frac{x^{a}-1}{x-1}$ using Fermat's little theorem
positive_passages.docid: 154217
positive_passages.text: Can't come even near to the solution.. Can somebody take a look?
negative_passages.docid: 81346
negative_passages.text: Let $r$ be the smallest positive integer such that $a^r \equiv 1 \bmod{n}$. Prove $r \mid \phi(n)$.
negative_passages.docid: 58133
negative_passages.text: ${a^2}{\mid}({b^3} + 1)\;$and$\;{b^2}{\mid}({a^3} + 1)$
negative_passages.docid: 42376
negative_passages.text: Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$
negative_passages.docid: 45171
negative_passages.text: How prove this $(p-1)!\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{p-1}\right)\equiv 0\pmod{p^2}$
negative_passages.docid: 149576
negative_passages.text: $x(a^{1/x}-1)$ is decreasing
negative_passages.docid: 3110
negative_passages.text: Prove $\frac{1}{\sqrt{x}}\geq \frac{\ln x}{x-1}$
negative_passages.docid: 65534
negative_passages.text: Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
negative_passages.docid: 96062
negative_passages.text: Show $\underbrace{{111\cdots}1}_{{\small{p-1} \ 1's}}$ is divisible by $p$
negative_passages.docid: 110876
negative_passages.text: Prove that $p\mid \binom{p}{k},\ 0< k< p$
negative_passages.docid: 93820
negative_passages.text: Fermat's little theorem applied for $n$'th root existence $\!\bmod p$
negative_passages.docid: 158863
negative_passages.text: How to prove $\sum_p p^{-2} < \frac{1}{2}$?
negative_passages.docid: 12100
negative_passages.text: $n \mid (a^{n}-b^{n}) \ \Longrightarrow$ $n \mid \frac{a^{n}-b^{n}}{a-b}$
negative_passages.docid: 146093
negative_passages.text: Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
negative_passages.docid: 77164
negative_passages.text: If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
negative_passages.docid: 107765
negative_passages.text: Prove that there exists two roots in $[-1,1]$
negative_passages.docid: 77351
negative_passages.text: How to use Fermat's little theorem to find $50^{50}\pmod{13}$?