query: number of solutions and rank
positive_passages.docid: 146984
positive_passages.text: Prove: Full Rank and a solution os linear system
negative_passages.docid: 57221
negative_passages.text: counting the number of elements in a conjugacy class of $S_n$
negative_passages.docid: 35066
negative_passages.text: Nature and number of solutions to $xy=x+y$
negative_passages.docid: 142538
negative_passages.text: The number of solutions to an $n^{th}$ order differential equation.
negative_passages.docid: 103197
negative_passages.text: number of distinct solution of Integral equation
negative_passages.docid: 97040
negative_passages.text: Question about an application of the Rank-Nullity theorem
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: 77595
negative_passages.text: Number of solutions of $x_1 + 2x_2 + 3x_3 + \cdots + n x_n = p$
negative_passages.docid: 20922
negative_passages.text: If all minors are $0$, the rank is at most $n-2$
negative_passages.docid: 64731
negative_passages.text: Determine $"a"$ for which the system has no solutions, infinitely many solutions, or has one solution
negative_passages.docid: 108941
negative_passages.text: Combinatorics Question Asking How Many Integer Solutions Given Different Restrictions
negative_passages.docid: 97908
negative_passages.text: Finding the no. of possible matrices given the order and limited no. of entries
negative_passages.docid: 93459
negative_passages.text: Number of permutations of unspecified length
negative_passages.docid: 144025
negative_passages.text: Number of Solutions in this Number Puzzle
negative_passages.docid: 74114
negative_passages.text: How to find the number of anti-symmetric relations?
negative_passages.docid: 48949
negative_passages.text: Solving a Diophantine equation with a large solution
negative_passages.docid: 114996
negative_passages.text: $x+y+z=n$. Finding the number of solutions.