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Category: Number Theory

Two-different-prime-numbers-between-4-and-18-are-chosen-When-their-sum-is-subtracted-from-their-product-then-a-number-x-is-obtained-which-is-a-multiple-of-17-Find-the-sum-of-digits-of-number-x-

Question Number 19631 by Tinkutara last updated on 13/Aug/17 $$\mathrm{Two}\:\mathrm{different}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{between} \\ $$$$\mathrm{4}\:\mathrm{and}\:\mathrm{18}\:\mathrm{are}\:\mathrm{chosen}.\:\mathrm{When}\:\mathrm{their}\:\mathrm{sum}\:\mathrm{is} \\ $$$$\mathrm{subtracted}\:\mathrm{from}\:\mathrm{their}\:\mathrm{product}\:\mathrm{then}\:\mathrm{a} \\ $$$$\mathrm{number}\:{x}\:\mathrm{is}\:\mathrm{obtained}\:\mathrm{which}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{multiple}\:\mathrm{of}\:\mathrm{17}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{digits}\:\mathrm{of} \\ $$$$\mathrm{number}\:{x}. \\ $$ Answered by ajfour…

What-is-the-digital-root-of-3-2017-

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

Assume-that-a-b-c-and-d-are-positive-integers-such-that-a-5-b-4-c-3-d-2-and-c-a-19-Determine-d-b-

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…

Find-a-natural-number-n-such-that-3-9-3-12-3-15-3-n-is-a-perfect-cube-of-an-integer-

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…

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…