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Category: Number Theory

The-sum-of-two-positive-integers-is-52-and-their-LCM-is-168-Find-the-numbers-

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-150223

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}}…

what-is-the-maximum-number-of-time-three-divides-333-505-

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}}…

Find-the-number-of-numbers-10-8-which-are-neither-perfect-squares-nor-perfect-cubes-nor-perfect-fifth-powers-

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}.…

Determine-the-smallest-positive-integer-x-whose-last-digit-is-6-and-if-we-erase-this-6-and-put-it-in-left-most-of-the-number-so-obtained-the-number-becomes-4x-

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…

Find-the-number-of-odd-integers-between-30-000-and-80-000-in-which-no-digit-is-repeated-

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} \\…

Show-that-for-any-natural-number-n-the-fraction-21n-4-14n-3-is-in-its-lowest-term-

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} \\…

How-many-times-is-digit-0-written-when-listing-all-numbers-from-1-to-3333-

Question Number 18498 by Tinkutara last updated on 22/Jul/17 $$\mathrm{How}\:\mathrm{many}\:\mathrm{times}\:\mathrm{is}\:\mathrm{digit}\:\mathrm{0}\:\mathrm{written}\:\mathrm{when} \\ $$$$\mathrm{listing}\:\mathrm{all}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{3333}? \\ $$ Commented by richard last updated on 23/Jul/17 $${do}\:{you}\:{want}\:{how}\:{many}\:{zeros}\:{there}\:{are}\:{between}\:\mathrm{1}\:{and}\:\mathrm{3333},\:{or}\:{how}\:{many}\:{times}\:{the}\:“\mathrm{0}''\:{appears},\:{independently}\:{of}\:{the}\:{amount}\:{of}\:{zeros}? \\ $$ Answered…