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Find-all-the-values-of-n-such-that-5-n-1-is-divisble-by-7-

Question Number 125471 by ZiYangLee last updated on 11/Dec/20 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:{n}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{5}^{{n}} +\mathrm{1}\:\mathrm{is}\:\mathrm{divisble}\:\mathrm{by}\:\mathrm{7}. \\ $$ Answered by MJS_new last updated on 11/Dec/20 $$\mathrm{try}\:\mathrm{for}\:\mathrm{the}\:\mathrm{first}\:\mathrm{few}\:{n}\:\Rightarrow\:{n}=\mathrm{3}+\mathrm{6}{n} \\ $$…

advanced-calculus-prove-that-I-1-t-4-6t-2-1-ln-ln-t-1-t-2-3-dt-2G-pi-G-catalan-constant-

Question Number 125462 by mnjuly1970 last updated on 11/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\clubsuit{advanced}\:\:{calculus}\clubsuit… \\ $$$$\:\:\:\blacklozenge\blacklozenge\:{prove}\:{that}: \\ $$$$\:\:\:\:\:\mathrm{I}=\int_{\mathrm{1}} ^{\:\infty} \frac{\left({t}^{\mathrm{4}} −\mathrm{6}{t}^{\mathrm{2}} +\mathrm{1}\right){ln}\left({ln}\left({t}\right)\right)}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{3}} }{dt}=\frac{\mathrm{2G}}{\pi} \\ $$$$\:\:\mathrm{G}\::\:\:{catalan}\:\:{constant}… \\ $$ Answered…

If-lim-x-3-3x-3-2x-4-2-A-andlim-x-3-3x-x-6-4x-8-1-x-pA-then-p-

Question Number 190996 by cortano12 last updated on 16/Apr/23 $$\:\:\:\mathrm{If}\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{3x}}−\mathrm{3}}{\:\sqrt{\mathrm{2x}−\mathrm{4}}−\sqrt{\mathrm{2}}}\:=\:\mathrm{A} \\ $$$$\:\:\:\mathrm{and}\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{3x}}+\mathrm{x}−\mathrm{6}}{\:\sqrt{\mathrm{4x}−\mathrm{8}}+\mathrm{1}−\mathrm{x}}\:=\:\mathrm{pA} \\ $$$$\:\:\:\mathrm{then}\:\mathrm{p}\:=?\: \\ $$ Commented by mustafazaheen last updated on 16/Apr/23…

In-a-room-containing-N-people-N-gt-3-at-least-one-person-has-not-shaken-hands-with-everyone-else-in-the-room-What-is-the-maximum-number-of-people-in-the-room-that-could-have-shaken-hands-with-ev

Question Number 125460 by john_santu last updated on 11/Dec/20 $$\:{In}\:{a}\:{room}\:{containing}\:{N}\:{people} \\ $$$${N}>\mathrm{3},\:{at}\:{least}\:{one}\:{person}\:{has}\:{not} \\ $$$${shaken}\:{hands}\:{with}\:{everyone} \\ $$$${else}\:{in}\:{the}\:{room}.\:{What}\:{is}\:{the}\: \\ $$$${maximum}\:{number}\:{of}\:{people}\: \\ $$$${in}\:{the}\:{room}\:{that}\:{could}\:{have}\: \\ $$$${shaken}\:{hands}\:{with}\:{everyone}\: \\ $$$${else}?\: \\…