query: Question 7.1 of Introduction to analytic number theory ( Apostol)
positive_passages.docid: 36
positive_passages.text: Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
negative_passages.docid: 14197
negative_passages.text: show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$
negative_passages.docid: 34710
negative_passages.text: Cardinality of Irrational Numbers
negative_passages.docid: 126574
negative_passages.text: Proving $\prod_k \sin \pi k / n = n / 2^{n-1}$
negative_passages.docid: 148247
negative_passages.text: Prove the existence of an analytic function
negative_passages.docid: 93581
negative_passages.text: On questions about the integral of the logarithm of the Riemann zeta function II
negative_passages.docid: 145879
negative_passages.text: $R$ is PID, so $R/I$ is PID, and application on $\mathbb{Z}$ and $\mathbb{N}$
negative_passages.docid: 61987
negative_passages.text: $x^2+1=0$ in $\mathbb{Z}_7$
negative_passages.docid: 11935
negative_passages.text: Is $\mathbb{Z} \left[ \frac{1+i \sqrt{7}}{2} \right]$ euclidean?
negative_passages.docid: 26894
negative_passages.text: Series Divergence - Apostol Calculus Vol I, Section 10.20 #7
negative_passages.docid: 11500
negative_passages.text: Divisibility by 7 rule, and Congruence Arithmetic Laws
negative_passages.docid: 62996
negative_passages.text: A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
negative_passages.docid: 153664
negative_passages.text: When is $\Bbb{Z[\zeta_n]}$ a PID?
negative_passages.docid: 55138
negative_passages.text: An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$
negative_passages.docid: 137711
negative_passages.text: Alternative proof that $[\Bbb{Q}(\zeta_n) : \Bbb{Q} ]= \varphi(n)$ uses circular reasoning?
negative_passages.docid: 118305
negative_passages.text: Let $p$ be an odd prime. $p$ and $(1-\zeta_p)^{p-1}$ are associates in $\mathbb{Z}[\zeta_p]$.
negative_passages.docid: 23523
negative_passages.text: Two problems on number theory