Question Number 212999 by golsendro last updated on 28/Oct/24 $$\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{non}\:\mathrm{zero}\:\mathrm{integer}\: \\ $$$$\:\mathrm{solution}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{to}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\:\:\:\:\frac{\mathrm{15}}{\mathrm{x}^{\mathrm{2}} \mathrm{y}}\:+\:\frac{\mathrm{3}}{\mathrm{xy}}\:−\:\frac{\mathrm{2}}{\mathrm{x}}\:=\:\mathrm{2}\: \\ $$ Answered by A5T last updated on 28/Oct/24 $$\frac{\mathrm{3}−\mathrm{2}{y}}{{xy}}=\mathrm{2}−\frac{\mathrm{15}}{{x}^{\mathrm{2}}…
Question Number 212890 by MrGaster last updated on 26/Oct/24 $$\mathrm{If}\:\mathrm{positive}\:\mathrm{integer}\:{x}+,{y}>\mathrm{1},{gcd}\left({x},{y}\right)=\mathrm{1}, \\ $$$$\mathrm{Positive}\:\mathrm{integer}\:\mathrm{n}\:\mathrm{satisfies}\:\mathrm{that}\:\mathrm{there}\:\mathrm{is}\: \\ $$$$\mathrm{nononnegative}\:\mathrm{integer}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{makes}\:\mathrm{n}={ax}+{by}\: \\ $$$$\mathrm{If}\:\mathrm{true}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{n} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212242 by York12 last updated on 08/Oct/24 $$\mathrm{Help} \\ $$ Commented by York12 last updated on 08/Oct/24 Commented by Frix last updated on…
Question Number 212201 by universe last updated on 06/Oct/24 $$\:\:\:\:\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{two}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{9}^{\mathrm{9}^{\mathrm{9}} } \:? \\ $$ Answered by A5T last updated on 06/Oct/24 $$\mathrm{9}^{\mathrm{9}} =\left(\mathrm{81}\right)^{\mathrm{4}} ×\mathrm{9}\equiv\mathrm{9}\left({mod}\:\mathrm{40}\right) \\…
Question Number 211943 by Frix last updated on 25/Sep/24 $$\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)…