Question

how many solutions are there to the equation x1 x2 x3 = 15, if each xi is a positive integer? use the method shown in example 9.6.5 to answer this question.

Answer 1

There are two possible solutions for the equation $x_{1}\cdot x_{2}\cdot x_{3} = 15$: (i) $\{1,1,15\}$, (ii) $\{1,1,15\}$.

If $x_{1}$, $x_{2}$ and $x_{3}$ are only positive integers, then they must be divisors of 15, whose set is presented below with the following four elements:

$D_{15} = \{1, 3, 5, 15\}$ (1)

Based on this information, there are only two possible solutions: (i) $\{1,1,15\}$, (ii) $\{1,1,15\}$.

There are two possible solutions for the equation $x_{1}\cdot x_{2}\cdot x_{3} = 15$: (i) $\{1,1,15\}$, (ii) $\{1,1,15\}$.

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Nota - As there is no reference to the example 9.6.5, we present an alternative useful method to find a solution.