Category: Arithmetic

Question Number 5834 by sanusihammed last updated on 31/May/16 $$Findallpositiveintegersnforwhichthereexist$$$$non-negativeinteger.a_1{a}_2{a}_3\dots \dots .a_n.Suchthat$$$$\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{1}} } }\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{2}} } }\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{3}} } }\:+\:….\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{{n}} }…

Question Number 71294 by Mohamed Amine Bouguezzoul last updated on 13/Oct/19 $$solvein\mathbb{Z}\frac{1}{x}+\frac{1}{y}=\frac{1}{p}withp\in \mathbb{P}$$ Commented by Rasheed.Sindhi last updated on 13/Oct/19 $$\frac{x+y}{xy}=\frac{1}{p}$$$$\frac{{xy}}{{x}+{y}}={p} \…

Question Number 136739 by Ar Brandon last updated on 25/Mar/21 $$\mathrm{Given}0<\mathrm{a}<\mathrm{b},\mathrm{prove}\mathrm{that}$$$$\frac{{(\mathrm{b}-\mathrm{a})}^2}{8\mathrm{b}}⩽\frac{\mathrm{a}+\mathrm{b}}{2}-\sqrt{\mathrm{ab}}⩽\frac{{(\mathrm{b}-\mathrm{a})}^2}{8\mathrm{a}}$$ 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 71115 by TawaTawa last updated on 11/Oct/19 Answered by mind is power last updated on 11/Oct/19 $$\mathrm{A}.\left(999994\right)\dots \dots \left(1000002\right)=1\left(1000003\right)$$$$\mathrm{used}\mathrm{wilson}\mathrm{theorem}(\mathrm{p}-1)!=1\left(\mathrm{p}\right)$$$$\Rightarrow$$$$\Rightarrow\mathrm{A}\left(−\mathrm{1}\right).\left(−\mathrm{2}\right)……\left(−\mathrm{9}\right)=\mathrm{1}\left(\mathrm{1000003}\right)…

Question Number 5519 by FilupSmith last updated on 17/May/16 $$P=\underset{i=1}{\prod ^n}\frac{a^i}{b^i}a\ne b,b\ne 0$$$$P=??$$ Commented by Yozzii last updated on 17/May/16…