Category: Arithmetic

Question Number 28932 by Rasheed.Sindhi last updated on 01/Feb/18 $$\mathrm{Determine}\mathrm{the}\mathrm{least}\mathrm{number}\mathrm{of}4\mathrm{digits},$$$$\mathrm{which}\mathrm{is}\mathrm{perfect}\mathrm{square}.$$$$\mathrm{Method}\mathrm{of}\mathrm{finding}\mathrm{is}\mathbf{required}.$$ Answered by mrW2 last updated on 01/Feb/18 $${x}={n}^{\mathrm{2}} \geqslant\mathrm{1000}…

Question Number 28805 by NECx last updated on 30/Jan/18 $$Inacompetition,aschoolawarded$$$$medalsindifferentcategories.$$$$36medalsindance,12indramatics$$$$and18medalsinmusic.Ifthese$$$$medalswenttototal45,andonly$$$$4personsgotmedalsinallthree$$$$catogories.Usingsetnotations,$$$${how}\:{many}\:{received}\:{in}\:{exactly} \…

Question Number 94297 by peter frank last updated on 17/May/20 Commented by mathmax by abdo last updated on 18/May/20 $$weknowthat{x}^2+y^2+z^2=0\Rightarrow x=y=z(forx,y,zreals)$$$${so}\:\left({e}\right)\:\Rightarrow{cosx}\:={cos}\left(\mathrm{2}{x}\right)={cos}\left(\mathrm{3}{x}\right)=\mathrm{0}…

Question Number 159750 by greg_ed last updated on 20/Nov/21 $$\mathbf{Prove}\mathbf{that}$$$$\sqrt{689\times 690\times 691+1}\mathbf{is}\mathbf{a}\mathbf{naturel}\mathbf{number}.$$ Commented by Rasheed.Sindhi last updated on 20/Nov/21 $$Plcheckthequestion,\sqrt{689\times 690\times 691+1}$$$${is}\:{not}\:{a}\:{natural}\:{number}. \…

Question Number 94097 by Rio Michael last updated on 16/May/20 $$\mathrm{find}\mathrm{all}\mathrm{integers}n\mathrm{for}\mathrm{which}13\mid 4(n^2+1).$$ Commented by Rasheed.Sindhi last updated on 17/May/20 $$Thissequivalentto:$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{13}\:\mid\left({n}^{\mathrm{2}} +\mathrm{1}\right)…