Category: Number Theory

Question Number 19389 by tawa tawa last updated on 10/Aug/17 $$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{digital}\mathrm{root}\mathrm{of}{3}^{2017}$$ Answered by allizzwell23 last updated on 10/Aug/17 $$1\times 9=9$$$$2\times 9=18=1+8=9$$$$\:\:\:\mathrm{3}×\mathrm{9}\:=\:\mathrm{27}\:=\:\mathrm{2}+\mathrm{7}\:=\:\mathrm{9}…

Question Number 19192 by Tinkutara last updated on 06/Aug/17 $$\mathrm{Find}\mathrm{a}\mathrm{natural}\mathrm{number}{}^{\prime }{\mathrm{n}}^{\prime }\mathrm{such}\mathrm{that}$$$$3^9+3^{12}+3^{15}+3^n\mathrm{is}\mathrm{a}\mathrm{perfect}\mathrm{cube}\mathrm{of}$$$$\mathrm{an}\mathrm{integer}.$$ Commented by Tinkutara last updated…

Question Number 150223 by KONE last updated on 10/Aug/21 Answered by CAIMAN last updated on 10/Aug/21 Answered by CAIMAN last updated on 10/Aug/21 $$\boldsymbol{{il}}\:\boldsymbol{{y}}\:\boldsymbol{{a}}\:\boldsymbol{{une}}\:\boldsymbol{{erreur}}\:\boldsymbol{{c}}'\boldsymbol{{est}}\:\boldsymbol{{plutot}}\:\boldsymbol{{im}}\left(\boldsymbol{{Z}}_{\mathrm{1}} +\boldsymbol{{Z}}_{\mathrm{2}}…

Question Number 18949 by Tinkutara last updated on 01/Aug/17 $$\mathrm{Find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{numbers}⩽{10}^8$$$$\mathrm{which}\mathrm{are}\mathrm{neither}\mathrm{perfect}\mathrm{squares},\mathrm{nor}$$$$\mathrm{perfect}\mathrm{cubes},\mathrm{nor}\mathrm{perfect}\mathrm{fifth}\mathrm{powers}.$$ Commented by prakash jain last updated on 03/Aug/17 $$\mathrm{i}\:\mathrm{retyped}\:\mathrm{the}\:\mathrm{answer}.…

Question Number 18884 by Tinkutara last updated on 31/Jul/17 $$\mathrm{Determine}\mathrm{the}\mathrm{smallest}\mathrm{positive}\mathrm{integer}$$$$\mathrm{x},\mathrm{whose}\mathrm{last}\mathrm{digit}\mathrm{is}6\mathrm{and}\mathrm{if}\mathrm{we}\mathrm{erase}$$$$\mathrm{this}6\mathrm{and}\mathrm{put}\mathrm{it}\mathrm{in}\mathrm{left}\mathrm{most}\mathrm{of}\mathrm{the}$$$$\mathrm{number}\mathrm{so}\mathrm{obtained},\mathrm{the}\mathrm{number}$$$$\mathrm{becomes}4\mathrm{x}.$$ Answered by mrW1 last updated…