query: Number of non negative integer solutions with additional restriction
positive_passages.docid: 146491
positive_passages.text: Number of solutions of $x_1+x_2+\dots+x_k=n$ with $x_i\le r$
negative_passages.docid: 62036
negative_passages.text: Finding the number of non-negative integral solutions of $x + y + z = 10$
negative_passages.docid: 45408
negative_passages.text: How many solutions does the equation $x_1 + x_2 + x_3 = 11$ have, where $x_1, x_2, x_3$ are nonnegative integers?
negative_passages.docid: 134352
negative_passages.text: The number of possible factorizations of a positive integer.
negative_passages.docid: 35066
negative_passages.text: Nature and number of solutions to $xy=x+y$
negative_passages.docid: 114996
negative_passages.text: $x+y+z=n$. Finding the number of solutions.
negative_passages.docid: 20713
negative_passages.text: The sum of an uncountable number of positive numbers
negative_passages.docid: 26081
negative_passages.text: What will be total number of solutions of $a+b+c = n$?
negative_passages.docid: 137652
negative_passages.text: How many solutions does the equation $n_1 + n_2 + n_3 + n_4 + n_5 = 20$ have in the positive integers if $n_1 < n_2 < n_3 < n_4 < n_5$?
negative_passages.docid: 15314
negative_passages.text: Number of solutions to $x^n \equiv 1 \mod p$
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: 24837
negative_passages.text: $x^2+1=0$ uncountable many solutions
negative_passages.docid: 118036
negative_passages.text: Proving at least 99 pairwise sums of the reals are non-negative
negative_passages.docid: 59419
negative_passages.text: Crafty solutions to the following limit
negative_passages.docid: 107964
negative_passages.text: Simple combinatorics problem.
negative_passages.docid: 24091
negative_passages.text: How many ways can $r$ nonconsecutive integers be chosen from the first $n$ integers?
negative_passages.docid: 73079
negative_passages.text: Eliminating non-integer solutions to $ab / (2\sqrt{ab} + a + b)$