Category: Algebra

Question Number 97428 by bobhans last updated on 08/Jun/20 Commented by Farruxjano last updated on 08/Jun/20 $$\mathit{I}\mathit{c}\mathit{o}\mathit{u}\mathit{l}\mathit{d}\mathit{n}\mathit{o}\mathit{t}\mathit{k}\mathit{n}\mathit{o}\mathit{w}\mathit{x}=1005\mathit{o}\mathit{r}\mathit{n}\mathit{o}\mathit{t}\mathit{i}\mathit{n}$$$$\mathit{m}\mathit{y}\mathit{s}\mathit{o}\mathit{l}\mathit{u}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{i}\mathit{f}\mathit{s}\mathit{o}\mathit{i}\mathit{t}\mathit{h}\mathit{i}\mathit{n}\mathit{k}\mathit{y}\mathit{o}\mathit{u}$$$$\mathit{c}\mathit{a}\mathit{n}\mathit{e}\mathit{a}\mathit{s}\mathit{i}\mathit{l}\mathit{y}\mathit{c}\mathit{a}\mathit{l}\mathit{c}\mathit{u}\mathit{l}\mathit{a}\mathit{t}\mathit{e}\mathit{r}\mathit{e}\mathit{m}\mathit{o}\mathit{v}\mathit{i}\mathit{n}\mathit{g}$$$$\mathit{x}\mathit{w}\mathit{i}\mathit{t}\mathit{h}1005,\mathit{s}\mathit{i}\mathit{r}$$$$…

Question Number 162942 by HongKing last updated on 02/Jan/22 $$\mathrm{How}\mathrm{many}\mathrm{positive}\mathrm{integers}\mathrm{less}\mathrm{than}$$$$500\mathrm{can}\mathrm{be}\mathrm{formed}\mathrm{using}\mathrm{the}\mathrm{numbers}$$$$1,2,3\mathrm{and}5\mathrm{for}\mathrm{the}\mathrm{digits}?$$ Answered by som(math1967) last updated on 02/Jan/22 $$\mathrm{3}\:{digitstarting}\:{with}\:\mathrm{1},\mathrm{2},\mathrm{3}\:=\mathrm{4}^{\mathrm{2}} ×\mathrm{3}…

Question Number 31868 by 6123 last updated on 16/Mar/18 $$Leta>b>1bepositiveintegerswithbodd.$$$$Letnbeapositiveintegeraswell.If{b}^{n}divides$$$$a^n-1,provethat{a}^b>\frac{3^n}{n}.$$$$Solutionplease.Thanksinadvance!!$$ Terms of Service…

Question Number 31864 by rahul 19 last updated on 16/Mar/18 $$Let{S}_n=\underset{k=1}{\sum ^{4n}}{(-1)}^{\frac{k(k+1)}{2}}{k}^2.$$$$Then{S}_{n}cantakethevalue\left(s\right)$$$$1)1056$$$$2)1088$$$$\left.\mathrm{3}\right)\:\mathrm{1120}…

Question Number 162876 by HongKing last updated on 01/Jan/22 $$\mathrm{Prove}\mathrm{that}:$$$$\underset{0}{\stackrel{\frac{\mathit{\pi }}{2}}{\int }}(\mathrm{xcot}\mathbf{x}\cdot {\mathrm{lncos}}^2\mathbf{x}+{\ln }^2\cos \mathbf{x})\mathrm{dx}=\frac{{\pi }^3}{24}$$ Terms of Service Privacy Policy Contact:…