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Question Number 171085 by balirampatel last updated on 07/Jun/22

$$43devidedbyxremainderisx-5howmanyvalueofx?$$

Answered by Rasheed.Sindhi last updated on 08/Jun/22

$$$$$$Assuming:$$$$1<divisor<43\wedge 0⩽remainder<43$$$$1<x<43\wedge 0⩽x-5<43$$$$\bullet 5⩽x<43.....................\left(\mathrm{i}\right)$$$$\frac{43-(x-5)}{x}=m\in \mathbb{N}$$$$48-x=mx$$$$\bullet (m+1)x=48\Rightarrow x\mid 48........\left(\mathrm{ii}\right)$$$$from\left(\mathrm{i}\right)\mathrm{\&}\left(\mathrm{ii}\right):$$$$x=6,8,12,16,24$$$$\begin{array}{|cc|}\hline \underset{x}{divisor}& \underset{x-5}{remainder}\\ 6& 1\\ 8& 3\\ 12& 7\\ 16& 11\\ 24& 19\\ \hline\end{array}$$

Commented by balirampatel last updated on 08/Jun/22

$$ThanksSir$$

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