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anemone
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Determine all triples of positive integers $x,\,y,\,z$ such that $z\ge y\ge x$ and $x+y+z+xy+yz+xz=xyz+1$.
anemone said:Determine all triples of positive integers $x,\,y,\,z$ such that $z\ge y\ge x$ and $x+y+z+xy+yz+xz=xyz+1$.
A positive integer solution is a set of values for variables in an equation that, when substituted, results in a positive integer value for the equation. In other words, it is a solution that satisfies the equation and has only positive whole numbers as its values.
To determine positive integer solutions, you can use a variety of methods such as algebraic manipulation, graphing, or trial and error. It is important to carefully analyze the given equation and use mathematical principles to solve for values that result in a positive integer solution.
No, there may not always be positive integer solutions for an equation. Some equations may have no solutions or only negative or fractional solutions. It depends on the specific equation and the values of its variables.
Yes, an equation can have multiple positive integer solutions. For example, the equation x + 3 = 7 has two positive integer solutions, x = 4 and x = 5. It is important to check all possible values to ensure all solutions are found.
Determining positive integer solutions can be useful in real-world situations where only whole numbers are applicable, such as in counting, measurements, or budgeting. It can also help in solving mathematical problems and proving mathematical theorems.