Question Number 227323 by CrispyXYZ last updated on 15/Jan/26 $$\mathrm{Is}\:\mathrm{there}\:\mathrm{an}\:{n}>\mathrm{11}\:\mathrm{such}\:\mathrm{that}\:\mathrm{every}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{2}^{{n}} \\ $$$$\mathrm{in}\:\mathrm{decimal}\:\mathrm{representation}\:\mathrm{is}\:\mathrm{even}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 227154 by gregori last updated on 03/Jan/26 $$ \left(\mathrm{202519}\right)^{\mathrm{2025}} \: \\ $$$$\: \\ $$ Answered by mahdipoor last updated on 03/Jan/26 $$\mathrm{202519}\equiv−\mathrm{2}\:\:\:\mathrm{mod}\left(\mathrm{17}\right) \\…
Question Number 227080 by Spillover last updated on 29/Dec/25 Answered by Kassista last updated on 29/Dec/25 $$\left.{a}\right)\:\underset{{x}\rightarrow−\mathrm{6}} {\mathrm{lim}}\:{f}\left({x}\right)\:=\:\underset{{x}\rightarrow−\mathrm{6}} {\mathrm{lim}}\:\mathrm{7}−\mathrm{4}{x}\:=\:\mathrm{7}−\mathrm{4}\left(−\mathrm{6}\right)=\:\mathrm{31} \\ $$$$ \\ $$$$\left.{b}\right)\:\underset{{x}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}\:{f}\left({x}\right)\:=\:\underset{{x}\rightarrow\mathrm{1}^{−}…
Question Number 225601 by gregori last updated on 04/Nov/25 $$\:\:\: \mathrm{2}^{\mathrm{2025}} ×\mathrm{3}^{\mathrm{2025}} \: \\ $$ Commented by mr W last updated on 04/Nov/25 $${the}\:{unit}\:{digit}\:{of}\:\mathrm{6}^{{n}} {is}\:{always}\:\mathrm{6}.…
Question Number 223480 by Bebe last updated on 26/Jul/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222974 by gabthemathguy25 last updated on 12/Jul/25 Answered by MrGaster last updated on 12/Jul/25 $${P}_{\mathrm{100}} =\mathrm{min}\left\{{x}\in\mathbb{N}\mid\underset{{k}=\mathrm{1}} {\overset{{x}} {\sum}}\underset{{i}=\mathrm{2}} {\overset{\lfloor\sqrt{{k}}\rfloor} {\prod}}\left(\mathrm{1}−\delta\left({k}\:\mathrm{mod}\:{i}\right)\right)\geq\mathrm{101}\right\} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{540}}…
Question Number 222635 by Mingma last updated on 02/Jul/25 Answered by Raphael254 last updated on 28/Jul/25 $${n}\:+\:{S}\left({n}\right)\:+\:{S}\left({S}\left({n}\right)\right)\:=\:\mathrm{2007} \\ $$$$ \\ $$$${n}\:=\:\mathrm{1983} \\ $$$$ \\ $$$$\mathrm{1983}\:+\:\left(\mathrm{1}+\mathrm{9}+\mathrm{8}+\mathrm{3}\right)\:+\:{S}\left(\mathrm{1}+\mathrm{9}+\mathrm{8}+\mathrm{3}\right)\:=…
Question Number 222516 by MrGaster last updated on 29/Jun/25 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{integer}\:{k},\mathrm{how}\:\:\mathrm{to} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{incomplete}\:\mathrm{general} \\ $$$$\mathrm{solution}\:\mathrm{for}\:\mathrm{the}\:\mathrm{non}-\mathrm{trivial}\:\mathrm{integer} \\ $$$$\mathrm{solutions}\:\mathrm{of}\:\:\mathrm{the}\:\mathrm{Diophantine}\:\mathrm{equation}: \\ $$$${a}^{\mathrm{4}} +{b}^{\mathrm{4}} +{ka}^{\mathrm{2}} {b}^{\mathrm{2}} ={c}^{\mathrm{4}} +{d}^{\mathrm{4}} +{kc}^{\mathrm{2}} {d}^{\mathrm{2}}…
Question Number 219732 by Spillover last updated on 01/May/25 Answered by Spillover last updated on 01/May/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219657 by Nicholas666 last updated on 30/Apr/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{prove}; \\ $$$$\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\left(\mathrm{5}{n}−\mathrm{2}\right)\left(\mathrm{5}{n}−\mathrm{3}\right)}{\left(\mathrm{5}{n}−\mathrm{1}\right)\left(\mathrm{5}{n}−\mathrm{4}\right)}\:=\:\varphi \\ $$$$ \\ $$ Answered by MrGaster last updated…