Question Number 19239 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Assume}\:\mathrm{that}\:{a},\:{b},\:{c}\:\mathrm{and}\:{d}\:\mathrm{are}\:\mathrm{positive} \\ $$$$\mathrm{integers}\:\mathrm{such}\:\mathrm{that}\:{a}^{\mathrm{5}} \:=\:{b}^{\mathrm{4}} ,\:{c}^{\mathrm{3}} \:=\:{d}^{\mathrm{2}} \:\mathrm{and} \\ $$$${c}\:−\:{a}\:=\:\mathrm{19}.\:\mathrm{Determine}\:{d}\:−\:{b}. \\ $$ Answered by ajfour last updated…
Question Number 19192 by Tinkutara last updated on 06/Aug/17 $$\mathrm{Find}\:\mathrm{a}\:\mathrm{natural}\:\mathrm{number}\:'\mathrm{n}'\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{3}^{\mathrm{9}} \:+\:\mathrm{3}^{\mathrm{12}} \:+\:\mathrm{3}^{\mathrm{15}} \:+\:\mathrm{3}^{{n}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{cube}\:\mathrm{of} \\ $$$$\mathrm{an}\:\mathrm{integer}. \\ $$ Commented by Tinkutara last updated…
Question Number 19193 by Tinkutara last updated on 06/Aug/17 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{is}\:\mathrm{52} \\ $$$$\mathrm{and}\:\mathrm{their}\:\mathrm{LCM}\:\mathrm{is}\:\mathrm{168}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{numbers}. \\ $$ Answered by RasheedSindhi last updated on 06/Aug/17 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\mathrm{and}\:\mathrm{their}\:\mathrm{HCF}\:\mathrm{is}\:\mathrm{h} \\…
Question Number 150223 by KONE last updated on 10/Aug/21 Answered by CAIMAN last updated on 10/Aug/21 Answered by CAIMAN last updated on 10/Aug/21 $$\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 19002 by tawa tawa last updated on 02/Aug/17 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{number}\:\mathrm{of}\:\:\mathrm{time}\:\mathrm{three}\:\mathrm{divides}\:\mathrm{333}^{\mathrm{505}} \\ $$ Answered by RasheedSindhi last updated on 03/Aug/17 $$\mathrm{333}=\mathrm{37}×\mathrm{3}^{\mathrm{2}} \\ $$$$\mathrm{333}^{\mathrm{505}} =\mathrm{37}^{\mathrm{505}} ×\left(\mathrm{3}^{\mathrm{2}}…
Question Number 18949 by Tinkutara last updated on 01/Aug/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{numbers}\:\leqslant\:\mathrm{10}^{\mathrm{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 $$\mathrm{i}\:\mathrm{retyped}\:\mathrm{the}\:\mathrm{answer}.…
Question Number 149962 by john_santu last updated on 08/Aug/21 $$\:\lfloor{x}\rfloor+\lfloor{y}\rfloor=\mathrm{43}.\mathrm{8}\:{and}\:{x}+{y}−\lfloor{x}\rfloor=\mathrm{18}.\mathrm{4} \\ $$$$.{Find}\:\mathrm{100}\left({x}+{y}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 18884 by Tinkutara last updated on 31/Jul/17 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\:\mathrm{integer} \\ $$$$\mathrm{x},\:\mathrm{whose}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{is}\:\mathrm{6}\:\mathrm{and}\:\mathrm{if}\:\mathrm{we}\:\mathrm{erase} \\ $$$$\mathrm{this}\:\mathrm{6}\:\mathrm{and}\:\mathrm{put}\:\mathrm{it}\:\mathrm{in}\:\mathrm{left}\:\mathrm{most}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{so}\:\mathrm{obtained},\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{becomes}\:\mathrm{4x}. \\ $$ Answered by mrW1 last updated…
Question Number 18655 by Tinkutara last updated on 26/Jul/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{odd}\:\mathrm{integers} \\ $$$$\mathrm{between}\:\mathrm{30},\mathrm{000}\:\mathrm{and}\:\mathrm{80},\mathrm{000}\:\mathrm{in}\:\mathrm{which}\:\mathrm{no} \\ $$$$\mathrm{digit}\:\mathrm{is}\:\mathrm{repeated}. \\ $$ Commented by mrW1 last updated on 27/Jul/17 $$\mathrm{let}'\mathrm{s}\:\mathrm{say}\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{XZZZY} \\…
Question Number 18652 by Tinkutara last updated on 26/Jul/17 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{natural}\:\mathrm{number}\:{n}, \\ $$$$\mathrm{the}\:\mathrm{fraction}\:\frac{\mathrm{21}{n}\:+\:\mathrm{4}}{\mathrm{14}{n}\:+\:\mathrm{3}}\:\mathrm{is}\:\mathrm{in}\:\mathrm{its}\:\mathrm{lowest}\:\mathrm{term}. \\ $$ Answered by diofanto last updated on 27/Jul/17 $$\mathrm{Lets}\:\mathrm{prove}\:\mathrm{by}\:\mathrm{contradiction}. \\ $$$$\mathrm{Suppose}\:\mathrm{there}\:\mathrm{is}\:{d}\:>\:\mathrm{1}\:\mathrm{such}\:\mathrm{that} \\…