Question Number 211943 by Frix last updated on 25/Sep/24 $$\mathrm{2}^{{m}−\mathrm{1}} =\mathrm{1}+{mn} \\ $$$${m},\:{n}\:\in\mathbb{Z} \\ $$ Commented by BHOOPENDRA last updated on 25/Sep/24 $$\left\{\left({m},{n}\right)\in\mathbb{Z}×\mathbb{Z}\:\mid\:{m}\:{is}\:{odd}\:\&{n}=\frac{\mathrm{2}^{{m}−\mathrm{1}} −\mathrm{1}}{{m}}\right\} \\…
Question Number 211635 by BaliramKumar last updated on 15/Sep/24 Answered by golsendro last updated on 15/Sep/24 $$\:\mathrm{10}^{\mathrm{31}} −\mathrm{5}−\mathrm{10}^{\mathrm{30}} −\mathrm{p}=\mathrm{10}^{\mathrm{30}} \left(\mathrm{10}−\mathrm{1}\right)−\left(\mathrm{5}+\mathrm{p}\right) \\ $$$$\:\mathrm{9}.\mathrm{10}^{\mathrm{3}} −\left(\mathrm{5}+\mathrm{p}\right)\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3} \\ $$$$\:\mathrm{so}\:\mathrm{p}=\mathrm{1}\:,\:\mathrm{4}\:,\:\mathrm{7}\:…
Question Number 211595 by BaliramKumar last updated on 14/Sep/24 Answered by mr W last updated on 14/Sep/24 $${m}^{\mathrm{2}} −{n}^{\mathrm{2}} =\mathrm{199} \\ $$$$\left({m}−{n}\right)\left({m}+{n}\right)=\mathrm{1}×\mathrm{199} \\ $$$${m}−{n}=\mathrm{1} \\…
Question Number 211454 by BaliramKumar last updated on 09/Sep/24 Answered by A5T last updated on 09/Sep/24 $${Let}\:{N}={p}_{\mathrm{1}} ^{\mathrm{2}} ×{p}_{\mathrm{2}} ^{\mathrm{4}} ;{then}\:{it}\:{has}\:\left(\mathrm{2}+\mathrm{1}\right)\left(\mathrm{4}+\mathrm{1}\right)=\mathrm{15}\:{divisors} \\ $$$$\Rightarrow{N}^{\mathrm{2}} ={p}_{\mathrm{1}} ^{\mathrm{4}}…
Question Number 211453 by BaliramKumar last updated on 09/Sep/24 Answered by A5T last updated on 09/Sep/24 $$\mathrm{5}^{{a}} \equiv\mathrm{5}\left({mod}\:\mathrm{10}\right);\mathrm{11}^{{c}} \equiv\mathrm{1}\left({mod}\:\mathrm{10}\right) \\ $$$$\Rightarrow\mathrm{5}^{{a}} +\mathrm{11}^{{c}} \equiv\mathrm{6}\left({mod}\:\mathrm{10}\right) \\ $$$$\mathrm{7}^{{b}}…
Question Number 211455 by BaliramKumar last updated on 09/Sep/24 Answered by BHOOPENDRA last updated on 10/Sep/24 $${Second}\:{hand}\:{T}_{{s}} =\mathrm{60}\:{sec} \\ $$$${minute}\:{hand}\:{T}_{{m}} =\mathrm{3600}\:{sec} \\ $$$${angular}\:{velocity} \\ $$$$\omega=\frac{\mathrm{2}\pi}{{T}}\:\left({where}\:{T}\:{is}\:{time}\:{period}\right)…
Question Number 211443 by BaliramKumar last updated on 09/Sep/24 Answered by A5T last updated on 09/Sep/24 $${Note}\:{that}\:{n}\leqslant\mathrm{10}\:{and}\:{cannot}\:{be}\:{composite} \\ $$$$\Rightarrow{It}\:{remains}\:{to}\:{check}\:{for}\:{n}=\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{7} \\ $$$$\mathrm{2}^{\mathrm{2}} −\mathrm{1}=\mathrm{3};\mathrm{2}^{\mathrm{3}} −\mathrm{1}=\mathrm{7};\mathrm{2}^{\mathrm{5}} −\mathrm{1}=\mathrm{31};\mathrm{2}^{\mathrm{7}} −\mathrm{1}=\mathrm{127}…
Question Number 211445 by BaliramKumar last updated on 09/Sep/24 Answered by A5T last updated on 09/Sep/24 $$={last}\:{three}\:{digits}\:{of}\:\mathrm{345}×\mathrm{789}=\mathrm{205}\Rightarrow\left({b}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 211456 by BaliramKumar last updated on 09/Sep/24 Answered by A5T last updated on 09/Sep/24 $${max}\:{when}\:\mathrm{8}{cos}\theta−\mathrm{8}{sin}\theta{cos}\theta=\mathrm{0} \\ $$$$\Rightarrow{cos}\theta=\mathrm{0}\:{or}\:{sin}\theta=\mathrm{1}\Rightarrow{max}=\mathrm{8}×\mathrm{1}−\mathrm{4}×\mathrm{1}=\mathrm{4} \\ $$ Answered by mehdee1342 last…
Question Number 208506 by Tawa11 last updated on 17/Jun/24 What is the smallest number which must added to 9454351626 so that it will become divisible…