Question Number 71852 by Rio Michael last updated on 21/Oct/19 $${show}\:{that}\:\mathrm{5}^{\mathrm{22}} \:+\:\mathrm{17}^{\mathrm{22}} \:\equiv\:\mathrm{6}\:\left({mod}\:\mathrm{11}\right) \\ $$ Answered by mind is power last updated on 21/Oct/19 $$\mathrm{ferma}\:\mathrm{little}\:\mathrm{theorem}…
Question Number 6317 by sanusihammed last updated on 23/Jun/16 $${Solve}\:{the}\:{system}\:{of}\:{equation}\: \\ $$$$ \\ $$$${x}\:+\:{y}\:−\:{z}\:=\:\mathrm{9}\:\:\:……….\:{equation}\:\left({i}\right) \\ $$$${x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}\:} +\:{z}^{\mathrm{2}\:} =\:\mathrm{99}\:\:………..\:{equation}\:\left({ii}\right) \\ $$$${y}^{\mathrm{2}} \:=\:{xz}\:\:\:………..\:{equation}\left({iii}\right) \\ $$ Commented…
Question Number 6316 by sanusihammed last updated on 23/Jun/16 $${How}\:{many}\:{idempotent}\:{matrices}\:{can}\:{be}\:{formed}\:{from}\:{a} \\ $$$${diagonal}\:{matrix}\:{A}\:{with}\:{the}\:{elements}\: \\ $$$${a}\left({i},{i}\right)\:{for}\:{i}\:=\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},…….{n}\right\} \\ $$ Answered by nburiburu last updated on 23/Jun/16 $$\:{in}\:\mathbb{R}^{{n}×{n}} :\:…
Question Number 71850 by SmNayon11 last updated on 21/Oct/19 $$\int\mathrm{ln}\left(\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } .\mathrm{e}^{\mathrm{x}^{\mathrm{x}} } \right)\mathrm{dx}=? \\ $$ Answered by MJS last updated on 21/Oct/19 $$\int\mathrm{ln}\:\left({x}^{{x}^{{x}} }…
Question Number 137384 by BHOOPENDRA last updated on 02/Apr/21 Commented by hei last updated on 02/Apr/21 $$ \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 71849 by device4438043516@gmail.com last updated on 23/May/20 $$ \\ $$ Answered by MJS last updated on 21/Oct/19 $${P}\:\:\:{Q}\:\:{P}\Rightarrow{Q}\:\:{P}\wedge{Q}\:\:{P}\wedge{Q}={P} \\ $$$$\mathrm{1}\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1} \\ $$$$\mathrm{1}\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0} \\…
Question Number 6311 by FilupSmith last updated on 23/Jun/16 $$\mathrm{According}\:\mathrm{to}\:\mathrm{WolframAlpha}: \\ $$$$\underset{{k}=\mathrm{0}} {\overset{{n}} {\prod}}\left(\mathrm{1}−{x}^{\left(−\mathrm{1}\right)^{{k}} } \right)=\left(\mathrm{1}−{x}\right)^{\lfloor\frac{{n}}{\mathrm{2}}\rfloor+\mathrm{1}} \left(\frac{{x}−\mathrm{1}}{{x}}\right)^{\lfloor\frac{{n}−\mathrm{1}}{\mathrm{2}}\rfloor+\mathrm{1}} \\ $$$$ \\ $$$$\mathrm{Can}\:\mathrm{anyone}\:\mathrm{work}\:\mathrm{out}\:\mathrm{how}? \\ $$ Commented by…
Question Number 137383 by bramlexs22 last updated on 02/Apr/21 $${What}\:{is}\:{the}\:{remainder}\:\mathrm{13}^{\mathrm{163}} \:{when} \\ $$$${divided}\:{by}\:\mathrm{99}\: \\ $$ Answered by EDWIN88 last updated on 02/Apr/21 $$\mathrm{By}\:\mathrm{Euler}\:\mathrm{Theorem}\: \\ $$$$\varphi\left(\mathrm{99}\right)\:=\:\mathrm{3}\left(\mathrm{3}−\mathrm{1}\right)\left(\mathrm{11}−\mathrm{1}\right)=\:\mathrm{60}\:…
Question Number 137382 by bramlexs22 last updated on 02/Apr/21 $${The}\:{solution}\:{set}\:{of}\:{equation} \\ $$$$\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{cos}\:^{\mathrm{2}} \mathrm{2}{x}+\mathrm{cos}\:^{\mathrm{2}} \mathrm{3}{x}\:=\:\mathrm{1}\: \\ $$$${on}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}\pi \\ $$ Commented by MJS_new last updated on…
Question Number 137376 by benjo_mathlover last updated on 02/Apr/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{9}}+\frac{\mathrm{1}}{\mathrm{15}}+\frac{\mathrm{1}}{\mathrm{25}}+…+\frac{\mathrm{1}}{\mathrm{45}}+\frac{\mathrm{1}}{\mathrm{75}}+…\:=? \\ $$ Answered by EDWIN88 last updated on 02/Apr/21 $$\begin{array}{|c|c|c|c|c|}{}&\hline{\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{0}} }}&\hline{\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{1}} }}&\hline{\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }}&\hline{\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }}&\hline{…}&\hline{\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{n}} }}&\hline{\underset{\mathrm{n}=\mathrm{0}}…