Question Number 202016 by sonukgindia last updated on 18/Dec/23
Answered by MM42 last updated on 18/Dec/23
$${x}^{\mathrm{55}} −\mathrm{1}=\mathrm{253}×\mathrm{8}{k}\Rightarrow``{x}''\:{is}\:{odd} \\ $$$$\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{54}} +{x}^{\mathrm{53}} +...+\mathrm{1}\right)=\mathrm{253}×\mathrm{8}{k} \\ $$$${x}−\mathrm{1}=\mathrm{8}{k}'\Rightarrow{x}\overset{\mathrm{8}} {\equiv}\mathrm{1} \\ $$