query: How many solutions are there to $x+y+z=n$? Need help understanding the answer.
positive_passages.docid: 27218
positive_passages.text: How to use stars and bars for solving number of integral solutions to an equality?
negative_passages.docid: 123159
negative_passages.text: Solutions of the diophantine equation $x+y+z=xyz$?
negative_passages.docid: 8446
negative_passages.text: Number of solutions over positive integers of $x_1 + x_2 + ... + x_n = S$ for $x_i \in [0, 25]$
negative_passages.docid: 10753
negative_passages.text: Natural number solutions to $\frac{xy}{x+y}=n$ (equivalent to $\frac 1x+\frac 1y=\frac 1n$)
negative_passages.docid: 82137
negative_passages.text: Given a, b How many solutions exists for x, such that: $a \bmod{x}=b $
negative_passages.docid: 117352
negative_passages.text: Show $x^n+ax+b=0$ has most two solutions
negative_passages.docid: 114379
negative_passages.text: Show that number of solutions satisfying $x^5=e$ is a multiple of 4?
negative_passages.docid: 15314
negative_passages.text: Number of solutions to $x^n \equiv 1 \mod p$
negative_passages.docid: 144025
negative_passages.text: Number of Solutions in this Number Puzzle
negative_passages.docid: 45616
negative_passages.text: Find all solutions of ${\frac {1} {x} } + {\frac {1} {y} } +{\frac {1} {z}}=1$, where $x$, $y$ and $z$ are positive integers
negative_passages.docid: 77533
negative_passages.text: What solutions does the equation 4x≡2mod10 have? (Hint, it will have more that one.) What about solutions to an equation ax≡dmodn, where d=gcd(a,n)?
negative_passages.docid: 50283
negative_passages.text: Find answer of $\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}=4$
negative_passages.docid: 57330
negative_passages.text: Find the number of solutions of $\sin x+2 \sin 2x- \sin 3x=3$
negative_passages.docid: 38541
negative_passages.text: How many solutions are there to $x_1 + x_2 + ... + x_5 = 21$?
negative_passages.docid: 16946
negative_passages.text: How many solutions for an equation with simple restrictions
negative_passages.docid: 83496
negative_passages.text: Math contest integer triplet problem: $x + y + z + xy + yz + xz = xyz − 1$
negative_passages.docid: 26081
negative_passages.text: What will be total number of solutions of $a+b+c = n$?