Question Number 92187 by jagoll last updated on 05/May/20
$$\mathrm{4x}\:=\:\mathrm{6}\:\left(\mathrm{mod}\:\mathrm{10}\:\right) \\ $$
Commented by john santu last updated on 05/May/20
$$\mathrm{4}×\mathrm{4}\:=\:\mathrm{16}\:=\:\mathrm{6}\:\left({mod}\:\mathrm{10}\right)\: \\ $$$$\mathrm{4}×\mathrm{9}\:=\:\mathrm{36}\:=\:\mathrm{6}\:\left({mod}\:\mathrm{10}\right)\: \\ $$$${then}\:\mathrm{4}\:\&\:\mathrm{9}\:\mathrm{is}\:\mathrm{solution}\: \\ $$
Answered by mr W last updated on 05/May/20
$$\mathrm{4}{x}=\mathrm{10}{n}+\mathrm{6}=\mathrm{8}{n}+\mathrm{4}+\mathrm{2}\left({n}+\mathrm{1}\right) \\ $$$${n}+\mathrm{1}=\mathrm{2}{k} \\ $$$${n}=\mathrm{2}{k}−\mathrm{1} \\ $$$$\mathrm{4}{x}=\mathrm{10}\left(\mathrm{2}{k}−\mathrm{1}\right)+\mathrm{6}=\mathrm{20}{k}−\mathrm{4} \\ $$$$\Rightarrow{x}=\mathrm{5}{k}−\mathrm{1}=\mathrm{4},\mathrm{9},\mathrm{14},\mathrm{19},.... \\ $$