Category: Number Theory

Question Number 212201 by universe last updated on 06/Oct/24 $$\mathrm{find}\mathrm{the}\mathrm{last}\mathrm{two}\mathrm{digits}\mathrm{of}{9}^{9^9}?$$ Answered by A5T last updated on 06/Oct/24 $$\mathrm{9}^{\mathrm{9}} =\left(\mathrm{81}\right)^{\mathrm{4}} ×\mathrm{9}\equiv\mathrm{9}\left({mod}\:\mathrm{40}\right) \…

Question Number 211635 by BaliramKumar last updated on 15/Sep/24 Answered by golsendro last updated on 15/Sep/24 $${10}^{31}-5-{10}^{30}-\mathrm{p}={10}^{30}(10-1)-(5+\mathrm{p})$$$$9.{10}^3-(5+\mathrm{p})\mathrm{divisible}\mathrm{by}3$$$$\:\mathrm{so}\:\mathrm{p}=\mathrm{1}\:,\:\mathrm{4}\:,\:\mathrm{7}\:…

Question Number 211454 by BaliramKumar last updated on 09/Sep/24 Answered by A5T last updated on 09/Sep/24 $$LetN=p_1^2\times p_2^4;thenithas(2+1)(4+1)=15divisors$$$$\Rightarrow{N}^{\mathrm{2}} ={p}_{\mathrm{1}} ^{\mathrm{4}}…

Question Number 211455 by BaliramKumar last updated on 09/Sep/24 Answered by BHOOPENDRA last updated on 10/Sep/24 $$Secondhand{T}_s=60sec$$$$minutehand{T}_m=3600sec$$$$angularvelocity$$$$\omega=\frac{\mathrm{2}\pi}{{T}}\:\left({where}\:{T}\:{is}\:{time}\:{period}\right)…

Question Number 211445 by BaliramKumar last updated on 09/Sep/24 Answered by A5T last updated on 09/Sep/24 $$=lastthreedigitsof345\times 789=205\Rightarrow \left(b\right)$$ Terms of Service Privacy Policy Contact:…