Question Number 71294 by Mohamed Amine Bouguezzoul last updated on 13/Oct/19 $${solve}\:{in}\:\mathbb{Z}\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}=\frac{\mathrm{1}}{{p}}\:{with}\:{p}\in\mathbb{P} \\ $$ Commented by Rasheed.Sindhi last updated on 13/Oct/19 $$\frac{{x}+{y}}{{xy}}=\frac{\mathrm{1}}{{p}} \\ $$$$\frac{{xy}}{{x}+{y}}={p} \\…
Question Number 5738 by FilupSmith last updated on 26/May/16 $$\mathrm{I}'\mathrm{m}\:\mathrm{having}\:\mathrm{trouble}\:\mathrm{understanding}\:\mathrm{why}: \\ $$$$\mathrm{2}^{−\mathrm{1}} \equiv\mathrm{3}\left(\mathrm{mod}\:\mathrm{5}\right) \\ $$$$ \\ $$$$\mathrm{Can}\:\mathrm{someone}\:\mathrm{explain},\:\mathrm{please}?\:\mathrm{Thank}\:\mathrm{you}! \\ $$ Commented by Rasheed Soomro last updated…
Question Number 136739 by Ar Brandon last updated on 25/Mar/21 $$\mathrm{Given}\:\mathrm{0}<\mathrm{a}<\mathrm{b},\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\left(\mathrm{b}−\mathrm{a}\right)^{\mathrm{2}} }{\mathrm{8b}}\leqslant\frac{\mathrm{a}+\mathrm{b}}{\mathrm{2}}−\sqrt{\mathrm{ab}}\leqslant\frac{\left(\mathrm{b}−\mathrm{a}\right)^{\mathrm{2}} }{\mathrm{8a}} \\ $$ Answered by snipers237 last updated on 26/Mar/21 $$\frac{{a}+{b}}{\mathrm{2}}−\sqrt{{ab}\:}=\:\frac{\left(\sqrt{{a}}−\sqrt{{b}}\right)^{\mathrm{2}}…
Question Number 5609 by FilupSmith last updated on 22/May/16 $$\lfloor{x}\rfloor\:=\:\mathrm{floor}\:\mathrm{function} \\ $$$$\lceil{x}\rceil\:=\:\mathrm{ceiling}\:\mathrm{function} \\ $$$$ \\ $$$$\mathrm{I}\:\mathrm{have}\:\mathrm{seen}\:\mathrm{somewhere}\:\mathrm{either}: \\ $$$$\lfloor{x}\rceil\:\:\mathrm{or}\:\:\lceil{x}\rfloor\:\:\:\left(\mathrm{i}\:\mathrm{dont}\:\mathrm{remember}\:\mathrm{which}\right) \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{it}/\mathrm{are}\:\mathrm{they}? \\ $$ Terms of Service…
Question Number 71115 by TawaTawa last updated on 11/Oct/19 Answered by mind is power last updated on 11/Oct/19 $$\mathrm{A}.\left(\mathrm{999994}\right)……\left(\mathrm{1000002}\right)=\mathrm{1}\left(\mathrm{1000003}\right) \\ $$$$\mathrm{used}\:\mathrm{wilson}\:\mathrm{theorem}\:\left(\mathrm{p}−\mathrm{1}\right)!=\mathrm{1}\left(\mathrm{p}\right) \\ $$$$\Rightarrow \\ $$$$\Rightarrow\mathrm{A}\left(−\mathrm{1}\right).\left(−\mathrm{2}\right)……\left(−\mathrm{9}\right)=\mathrm{1}\left(\mathrm{1000003}\right)…
Question Number 136640 by jahar last updated on 24/Mar/21 $${if}\:\frac{{x}+{y}}{\mathrm{3}{a}−{b}}=\:\frac{{y}+{z}}{\mathrm{3}{b}−{c}}=\frac{{z}+{x}}{\mathrm{3}{c}−{a}}\:{then}\: \\ $$$${prove}\:{that}\:,\frac{{x}+{y}+{z}}{{a}+{b}+{c}}\:=\:\:\:\frac{{ax}+{by}+{cz}}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 5519 by FilupSmith last updated on 17/May/16 $${P}=\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}\frac{{a}^{{i}} }{{b}^{{i}} }\:\:\:\:\:\:\:\:{a}\neq{b},\:{b}\neq\mathrm{0} \\ $$$${P}=?? \\ $$ Commented by Yozzii last updated on 17/May/16…
Question Number 136516 by metamorfose last updated on 22/Mar/21 $${find}\:{all}\:{integers}\:\left({x},{y}\right)\::\:\mathrm{5}^{{x}} =\mathrm{3}^{{x}} +\mathrm{2021}{y} \\ $$ Answered by MJS_new last updated on 23/Mar/21 $$\mathrm{solution}:\:{x}=\mathrm{322}{n}\wedge{y}=\frac{\mathrm{5}^{\mathrm{322}{n}} −\mathrm{3}^{\mathrm{322}{n}} }{\mathrm{2021}}\forall{n}\in\mathbb{N} \\…
Question Number 136500 by rexford last updated on 22/Mar/21 Answered by Dwaipayan Shikari last updated on 22/Mar/21 $${a}−\mathrm{2}{d}+{a}−{d}+{a}+{a}+{d}+{a}+\mathrm{2}{d}+{a}+\mathrm{3}{d}=\mathrm{78} \\ $$$$\Rightarrow\mathrm{6}{a}+\mathrm{3}{d}=\mathrm{78}\Rightarrow\mathrm{2}{a}+{d}=\mathrm{26} \\ $$$${since}\:{a}−\mathrm{2}{d}>\mathrm{1}\Rightarrow{a}>\mathrm{2}{d}+\mathrm{1}\:\:{Greatest}\:{possible}\:{when}\:{a}=\mathrm{2}{d}+\mathrm{1} \\ $$$$\mathrm{2}{a}+{d}=\mathrm{26}\Rightarrow\mathrm{5}{d}+\mathrm{2}=\mathrm{26}\Rightarrow\Rightarrow{d}=\frac{\mathrm{24}}{\mathrm{5}} \\…
Question Number 136478 by liberty last updated on 22/Mar/21 Terms of Service Privacy Policy Contact: info@tinkutara.com