Question Number 166601 by Rasheed.Sindhi last updated on 23/Feb/22 $${What}\:{is}\:{the}\:{condition}\:{that}\: \\ $$$${a}\:\boldsymbol{{palindrome}}-\boldsymbol{{number}} \\ $$$$\:{is}\:\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\mathrm{11}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 166602 by Rasheed.Sindhi last updated on 23/Feb/22 $$\mathcal{D}{etermine}\:{condition}/{s}\:{that} \\ $$$${a}\:\boldsymbol{{number}}\:\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\mathrm{11} \\ $$$${is}\:{a}\:\boldsymbol{{palindrome}}-\boldsymbol{{number}}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 101043 by bobhans last updated on 30/Jun/20 $$\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{11}} }\:+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{11}} }\:+\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{11}} }\:+\:…}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{11}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{11}} }−\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{11}} }+…}\:=? \\ $$ Answered by john santu last updated on…
Question Number 166530 by amin96 last updated on 21/Feb/22 Answered by qaz last updated on 22/Feb/22 $$\mathrm{6}\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2n}\right)!}{\left(\mathrm{n}!\right)^{\mathrm{2}} \mathrm{2}^{\mathrm{4n}+\mathrm{1}} \left(\mathrm{2n}+\mathrm{1}\right)} \\ $$$$=\mathrm{3}\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\begin{pmatrix}{\mathrm{2n}}\\{\mathrm{n}}\end{pmatrix}\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{2n}}…
Question Number 166475 by Rasheed.Sindhi last updated on 20/Feb/22 $$\mathcal{F}{ind}\:{out}\:{n}\in\mathbb{N} \\ $$$$\:{such}\:{that} \\ $$$${n}^{\mathrm{2}} +{n}\:{is}\:{divisible}\:{by}\:\mathrm{30}. \\ $$ Commented by mr W last updated on 20/Feb/22…
Question Number 100888 by bramlex last updated on 29/Jun/20 $${Find}\:{all}\:{pairs}\:\left({k},{n}\right)\:{of}\:{positive}\: \\ $$$${integer}\:{for}\:{which}\:\mathrm{7}^{{k}} −\mathrm{3}^{{n}} \:{divides} \\ $$$${k}^{\mathrm{4}} +{n}^{\mathrm{2}} \:. \\ $$ Terms of Service Privacy Policy…
Question Number 100733 by john santu last updated on 28/Jun/20 $$\mathrm{A}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{such}\:\mathrm{as}\:\mathrm{4334}\:\mathrm{is} \\ $$$$\mathrm{a}\:\mathrm{palindrome}\:\mathrm{if}\:\mathrm{it}\:\mathrm{reads}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{forwards}\:\mathrm{or}\:\mathrm{backwards}.\:\mathrm{What}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{only}\:\mathrm{prime}\:\mathrm{palindrome}\:\mathrm{with}\:\mathrm{an} \\ $$$$\mathrm{even}\:\mathrm{number}\:\mathrm{of}\:\mathrm{digits}?\: \\ $$ Commented by Rasheed.Sindhi last…
Question Number 100677 by bobhans last updated on 28/Jun/20 $$\mathrm{for}\:\mathrm{m},\mathrm{n}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{m}\:>\:\mathrm{n}\: \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{lcd}\left(\mathrm{m},\mathrm{n}\right)\:+\:\mathrm{lcd}\left(\mathrm{m}+\mathrm{1},\mathrm{n}+\mathrm{1}\right)\:>\:\frac{\mathrm{2mn}}{\:\sqrt{\mathrm{m}−\mathrm{n}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 35072 by Rasheed.Sindhi last updated on 15/May/18 $$\mathrm{An}\:\mathrm{n}-\mathrm{digit}\:\mathrm{decimal}\:\mathrm{number}\:\mathrm{has}\:\mathrm{been} \\ $$$$\mathrm{conveerted}\:\mathrm{into}\:\mathrm{octal}\:\mathrm{number}.\mathrm{Say}\:\mathrm{it} \\ $$$$\mathrm{has}\:\mathrm{m}\:\mathrm{digits}.\mathrm{What}\:\mathrm{are}\:\mathrm{possible}\:\:\mathrm{minimum}\: \\ $$$$\mathrm{and}\:\mathrm{maximum}\:\mathrm{values}\:\mathrm{of}\:\mathrm{m}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of} \\ $$$$\mathrm{n}? \\ $$ Commented by candre last updated…
Question Number 35071 by Rasheed.Sindhi last updated on 15/May/18 $$\mathrm{A}\:\mathrm{20}-\mathrm{digit}\:\mathrm{decimal}\:\mathrm{number}\:\mathrm{has}\:\mathrm{been} \\ $$$$\mathrm{converted}\:\mathrm{into}\:\mathrm{octal}\:\mathrm{system}.\mathrm{Say}\:\mathrm{it}\:\mathrm{has}\: \\ $$$$\mathrm{n}\:\mathrm{digits}.\:\mathrm{What}\:\mathrm{can}\:\mathrm{be}\:\mathrm{minimum}\:\mathrm{and} \\ $$$$\mathrm{maximum}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n}? \\ $$$$ \\ $$ Answered by candre last updated…