Category: Number Theory

Question Number 27816 by Rasheed.Sindhi last updated on 15/Jan/18 $$\mathrm{If}\mathrm{N}\mathrm{is}\mathbf{perfect}\mathbf{nth}\mathbf{power},\mathrm{prove}\mathrm{that}$$$$\mathrm{n}\mid (\mathrm{d}\left(\mathrm{N}\right)-1)$$$$[Where\mathrm{d}\left(\mathrm{N}\right)denotes\mathit{n}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}$$$$\mathit{o}\mathit{f}\mathit{d}\mathit{i}\mathit{v}\mathit{i}\mathit{s}\mathit{o}\mathit{r}\mathit{s}\mathit{o}\mathit{f}\mathrm{N}]$$$$\mathrm{Also}\mathrm{show}\mathrm{by}\mathrm{an}\mathrm{example}\mathrm{that}\mathrm{its}$$$$\mathrm{vice}\mathrm{versa}\mathrm{is}\mathrm{not}\mathrm{necessarily}\mathrm{correct}.$$ Commented by Rasheed.Sindhi…

Question Number 93241 by Ayod 19 last updated on 12/May/20 $${(1+\frac{1}{\mathrm{x}})}^{\mathrm{x}+1}={(1+\frac{1}{2019})}^{2019}$$$$\mathrm{Find}\mathrm{all}\mathrm{possible}\mathrm{values}\mathrm{of}x$$ Answered by prakash jain last updated on 12/May/20 $${x}=−\mathrm{2020}…

Question Number 27404 by sirigidiravikumar@gmail.com last updated on 06/Jan/18 $$\left(1\right).themeanof14.9.22.14.22.18$$ Answered by Rasheed.Sindhi last updated on 06/Jan/18 $$\frac{9+14\times 2+18+22\times 2}{6}=\frac{33}{2}$$ Terms of Service…

Question Number 158270 by Raxreedoroid last updated on 01/Nov/21 $$82,1336,18670,240004,2933338,34666672,400000006,?$$$$\mathrm{is}\mathrm{there}\mathrm{a}\mathrm{valid}\mathrm{pattern}\mathrm{for}\mathrm{these}\mathrm{numbers}?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 92453 by jagoll last updated on 07/May/20 $$\sqrt[\mathrm{i}]{\mathrm{i}}?$$ Commented by john santu last updated on 07/May/20 $${i}\:=\:{e}^{\frac{\pi{i}}{\mathrm{2}}} \:\Rightarrow\:\sqrt[{{i}\:\:}]{\:{i}}\:=\:\left({e}\right)^{\frac{\pi{i}}{\mathrm{2}}×\frac{\mathrm{1}}{{i}}} \:=\:{e}^{\frac{\pi}{\mathrm{2}}} \: \…