Question and Answers Forum

All Questions      Topic List

Number Theory Questions

Previous in All Question      Next in All Question      

Previous in Number Theory      Next in Number Theory      

Question Number 91448 by Cynosure last updated on 30/Apr/20

$$provethat1+x^{111}+x^{222}+x^{333}+x^{444}divides1+x^{111}+x^{222}+x^{333}+.......+x^{999}$$

Commented by Cynosure last updated on 30/Apr/20

$$plshelpmeonthis$$

Commented by Prithwish Sen 1 last updated on 30/Apr/20

$$\mathrm{putting}{\mathrm{x}}^{111}=\mathrm{a}$$$$\mathrm{then}\frac{1+\mathrm{a}+{\mathrm{a}}^2+.....+{\mathrm{a}}^9}{1+\mathrm{a}+{\mathrm{a}}^2+{\mathrm{a}}^3+{\mathrm{a}}^4}=\frac{1-{\mathrm{a}}^{10}}{1-{\mathrm{a}}^5}=\frac{1-{\left({\mathrm{a}}^5\right)}^2}{1-{\mathrm{a}}^5}=1+{\mathrm{a}}^5$$$$=1+{\mathbf{x}}^{555}\mathbf{proved}.$$

Commented by Cynosure last updated on 30/Apr/20

$$$$$$$$$$ithinkitshouldbesolvedinthismanner$$$$\mathrm{then}\frac{1+\mathrm{a}+{\mathrm{a}}^2+.....+{\mathrm{a}}^9}{1+\mathrm{a}+{\mathrm{a}}^2+{\mathrm{a}}^3+{\mathrm{a}}^4}=\frac{{\mathrm{a}}^{10}-1}{{\mathrm{a}}^5-1}=\frac{{\left({\mathrm{a}}^5\right)}^2-1}{a^5-1}={\mathrm{a}}^5+1$$$$$$$$$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com