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Question Number 92211 by jagoll last updated on 05/May/20

$$4\mathrm{x}=2\left(\mathrm{mod}3\right)$$

Commented by jagoll last updated on 05/May/20

$$\mathrm{x}=3\mathrm{k}-1$$$$\mathrm{x}=2,5,8,11,14,...$$

Answered by Rio Michael last updated on 07/May/20

$$4x\equiv 2\left(\mathrm{mod}3\right)$$$$\mathrm{here}\mathrm{we}\mathrm{still}\mathrm{have}\mathrm{one}\mathrm{solution}$$$$\mathrm{since}4\mathrm{and}3\mathrm{are}\mathrm{relatively}\mathrm{prime}.$$$$4=1\left(3\right)+1$$$$4=3\left(1\right)+0$$$$\Rightarrow 1=4-3$$$$1+3=4$$$$\mathrm{multiplicative}\mathrm{inverse}\mathrm{is}1.$$$$1\times 4x\equiv 1\times 2\left(\mathrm{mod}3\right)$$$$x\equiv 2\left(\mathrm{mod}3\right)\mathrm{should}\mathrm{be}\mathrm{our}\mathrm{only}\mathrm{solution}$$$$$$

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