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Question Number 137 by novrya last updated on 25/Jan/15

$$Solve2x\equiv 6\left(mod8\right)$$

Answered by mreddy last updated on 10/Dec/14

$$\gcd (2,8)=2,2\mathrm{divides}6$$$$\mathrm{So}\mathrm{there}\mathrm{are}2\mathrm{distinct}\mathrm{solutions}$$$$\mathrm{Solutions}\mathrm{for}x\mathrm{are}\mathrm{given}\mathrm{by}\mathrm{equation}$$$$2x+8y=6$$$$\mathrm{The}\mathrm{equation}2x+8y=6\mathrm{has}\mathrm{valid}\mathrm{solutions}\mathrm{for}$$$$x=3,x=7$$$$\mathrm{S}o\mathrm{the}\mathrm{solutions}\mathrm{for}2x\equiv 6\left(mod8\right)\mathrm{are}$$$$3\left(\mathrm{mod}8\right)\mathrm{and}7\left(\mathrm{mod}8\right)$$

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