query: Number of distinct integer-valued vector solution for $x_1 + x_2 + ... + x_r = n$
positive_passages.docid: 65763
positive_passages.text: Number of ways to write n as a sum of k nonnegative integers
negative_passages.docid: 32463
negative_passages.text: $ax\equiv b\pmod{\! n}$ has a unique solution if $\gcd(a,n) = 1$
negative_passages.docid: 112575
negative_passages.text: Finding integer solutions of $m^2-n^5 = m - n$
negative_passages.docid: 71108
negative_passages.text: Is there an integer $N>0$ such that $\varphi(n) = N$ has infinitely many solutions?
negative_passages.docid: 23866
negative_passages.text: Do there exist an infinite number of integer-solutions $(x,y,z)$ of $x^x\cdot y^y=z^z$ where $1\lt x\le y$?
negative_passages.docid: 56528
negative_passages.text: On the proof of existence and uniqueness of radix representation
negative_passages.docid: 77595
negative_passages.text: Number of solutions of $x_1 + 2x_2 + 3x_3 + \cdots + n x_n = p$
negative_passages.docid: 946
negative_passages.text: How to find solutions of linear Diophantine ax + by = c?
negative_passages.docid: 154610
negative_passages.text: Number of solutions for the given equation in finite field of order 32.
negative_passages.docid: 67899
negative_passages.text: Integer squares of the form $x^4+x^3+x^2+x+1$
negative_passages.docid: 33314
negative_passages.text: How many non-negative integer solutions does $x_1+x_2+\cdots+x_n=A$ have?
negative_passages.docid: 35712
negative_passages.text: Solve for n: $\varphi(2n)=\varphi(3n)$
negative_passages.docid: 39993
negative_passages.text: Count the number of positive solutions for a linear diophantine equation
negative_passages.docid: 117352
negative_passages.text: Show $x^n+ax+b=0$ has most two solutions
negative_passages.docid: 144769
negative_passages.text: Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$
negative_passages.docid: 14773
negative_passages.text: Finding distinct solutions for the equation
negative_passages.docid: 139350
negative_passages.text: Given two coprime integers, find multiples of them that differ by 1