Question

Question: -If $\left(\mathbf{m}\mathbf{,}\mathbf{n}\right)\mathbf{=}\mathbf{1}$and $\frac{\mathbf{m}}{\mathbf{d}}\mathbf{,}\frac{\mathbf{n}}{\mathbf{d}}$,prove that [Hint: -If$\mathbf{d}\mathbf{=}\mathbf{mk}$ then$\frac{\mathbf{n}}{\mathbf{mk}}$ use theorem ]

Short answer

Answer: -

It is proved that$\text{mn|d}$:

Step-by-step solution

Determine the common factors

Consider the relation:

m|d

Then:

d = mk ….. (1)

Then getting:

n|mk ….. (2)

Since, the value is: .

There are no common factors between the values of mand n.

So, n|k .

Then, k = nl .

Prove the statement

Substitute the values in the second equation for the value ofk .

Then, obtaining as:$d=\left(mn\right)l$.

It means that the value of d is multiple of mn .

Therefore, it is proved that: $mn|d$.