Question Number 3172 by Rasheed Soomro last updated on 07/Dec/15 $$\mathcal{H}{ow}\:{many}\:{different}\:\:{clock}−{type}\:{dials}\:{can}\:{be}\:{made}\: \\ $$$${containing}\:{first}\:{n}\:{natual}\:{numbers}\:{with}\:{the}\:{property} \\ $$$${that}\:{sum}\:{of}\:\:{any}\:{two}\:{numbers}\:{of}\:{consecutive}\:{positions}\:{be} \\ $$$${a}\:{prime}\:{number}. \\ $$$$\mathbb{N}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},…\right\} \\ $$ Commented by Rasheed Soomro…
Question Number 3146 by Rasheed Soomro last updated on 06/Dec/15 $$\mathcal{C}{hange}\:{the}\:{order}\:{of}\:{numbers}\:{on}\:{a}\:{clock}−{dial}\:{so}\:{that}\: \\ $$$${sum}\:{of}\:{any}\:{two}\:{numbers}\:\:{of}\:{consecutive}\:{positions}\:{may} \\ $$$${be}\:{prime}. \\ $$ Answered by prakash jain last updated on 06/Dec/15…
Question Number 134208 by liberty last updated on 01/Mar/21 $$\mathrm{Determine}\:\mathrm{if}\:\mathrm{the}\:\mathrm{series}\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\mathrm{a}_{\mathrm{n}} \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{formula}\:\mathrm{converges}\:\mathrm{or}\: \\ $$$$\mathrm{diverges}\:.\:\mathrm{a}_{\mathrm{1}} =\:\mathrm{7},\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:=\:\frac{\mathrm{9n}+\mathrm{3sin}\:\mathrm{n}}{\mathrm{4n}+\mathrm{5cos}\:\mathrm{n}}.\mathrm{a}_{\mathrm{n}} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{converges} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{diverges} \\ $$$$ \\…
Question Number 134069 by john_santu last updated on 27/Feb/21 $${Given}\:{a},{b}\:{and}\:{c}\:{are}\:{real}\:{numbers}\:{and}\:{a}<{b}<{c}. \\ $$$${If}\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:=\:\frac{\mathrm{1}}{\mathrm{18}}\:,\:{find}\:{minimum}\:{value}\:{of}\:{a}. \\ $$ Commented by mr W last updated on 27/Feb/21 $${no}\:{minimum}\:{for}\:{a}\:{exists}. \\ $$…
Question Number 134037 by benjo_mathlover last updated on 26/Feb/21 Answered by john_santu last updated on 27/Feb/21 $$\mathrm{49}^{\mathrm{303}} .\mathrm{3993}^{\mathrm{202}} .\mathrm{39}^{\mathrm{606}} \:= \\ $$$$\left(\mathrm{7}^{\mathrm{2}} \right)^{\mathrm{303}} .\:\mathrm{3}^{\mathrm{606}} .\mathrm{13}^{\mathrm{606}}…
Question Number 2878 by Yozzi last updated on 29/Nov/15 $${How}\:{many}\:{ordered}\:{pairs}\:\left({m},{n}\right)\:{are}\:{there} \\ $$$${for}\:\mathrm{1}\leqslant{m},{n}\leqslant\mathrm{100}\:{such}\:{that}\:\mathrm{7}^{{m}} +\mathrm{7}^{{n}} \\ $$$${is}\:{divisble}\:{by}\:\mathrm{5}? \\ $$ Commented by prakash jain last updated on 29/Nov/15…
Question Number 2842 by Yozzi last updated on 28/Nov/15 $${Prove}\:{that}\:\pi=\mathrm{3}.\mathrm{14}…\:{is}\:{irrational}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 133897 by bemath last updated on 25/Feb/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{positive}\:\mathrm{integer} \\ $$$$\mathrm{that}\:\mathrm{leaves}\:\mathrm{a}\:\mathrm{remainder}\:\mathrm{3}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{7} \\ $$$$,\:\mathrm{4}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{9}\:,\:\mathrm{and}\:\mathrm{8}\:\mathrm{when} \\ $$$$\mathrm{divided}\:\mathrm{by}\:\mathrm{11}. \\ $$ Answered by john_santu last updated on 25/Feb/21…
Question Number 2820 by Yozzis last updated on 27/Nov/15 $${We}\:{have}\:{the}\:{idea}\:{of}\:{Phythagorian}\:{triples} \\ $$$${as}\:{solutions}\:\left({x},{y},{z}\right)\:{to}\:{the}\:{equation} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={z}^{\mathrm{2}} \\ $$$${where}\:{x},{y},{z}\in\mathbb{Z}^{+} .\: \\ $$$${How}\:{frequently}\:{do}\:{solutions}\:\left({x},{y},{z},{t}\right)\:\:{to}\:{the}\:{equation} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}}…
Question Number 2815 by prakash jain last updated on 28/Nov/15 $$\eta\left({s}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{{s}} }\:\mathrm{Dirichlet}\:\mathrm{eta}\:\mathrm{function} \\ $$$$\mathrm{prove}\:\mathrm{that} \\ $$$$\eta\left({s}\right)=\left(\mathrm{1}−\mathrm{2}^{\mathrm{1}−{s}} \right)\zeta\left({s}\right) \\ $$ Commented by prakash…