query: How many solutions exists for this equation?
positive_passages.docid: 21531
positive_passages.text: The number of nonnegative integer triples with sum equal to $12$
negative_passages.docid: 144025
negative_passages.text: Number of Solutions in this Number Puzzle
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: 114379
negative_passages.text: Show that number of solutions satisfying $x^5=e$ is a multiple of 4?
negative_passages.docid: 124505
negative_passages.text: Proof that there must exist infinitely many solutions to a homogeneous system of equations when more unknowns than equations
negative_passages.docid: 14773
negative_passages.text: Finding distinct solutions for the equation
negative_passages.docid: 90261
negative_passages.text: Find all solutions of the equation $n^m=x^2+py^2$ which satisfy the following properties
negative_passages.docid: 146491
negative_passages.text: Number of solutions of $x_1+x_2+\dots+x_k=n$ with $x_i\le r$
negative_passages.docid: 89590
negative_passages.text: The number of solutions of $ax^2+by^2\equiv 1\pmod{p}$ is $ p-\left(\frac{-ab}{p}\right)$
negative_passages.docid: 62036
negative_passages.text: Finding the number of non-negative integral solutions of $x + y + z = 10$
negative_passages.docid: 44354
negative_passages.text: Total number of solutions of an equation
negative_passages.docid: 151732
negative_passages.text: Number of solutions of polynomials in a field
negative_passages.docid: 103304
negative_passages.text: Finding the number of solutions to a diophantine equation
negative_passages.docid: 82571
negative_passages.text: Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 67249
negative_passages.text: Can you determine a formula for this problem?
negative_passages.docid: 113407
negative_passages.text: Finding all solutions for a system of equations with constraint on the sum of absolute values
negative_passages.docid: 72857
negative_passages.text: Find the number of integral solutions of $2x + y + z = 20$?