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Category: Number Theory

Question-150965

Question Number 150965 by EDWIN88 last updated on 17/Aug/21 Answered by john_santu last updated on 17/Aug/21 $$\mathrm{R}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}\:_{\mathrm{10}} \mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{P}^{\mathrm{2}} \\ $$$$\mathrm{S}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}\:_{\mathrm{10}} \mathrm{y}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{Q}^{\mathrm{2}} \\ $$$$\Leftrightarrow\mathrm{P}+\mathrm{Q}+\mathrm{R}+\mathrm{S}\:=\:\mathrm{24}\: \\ $$$$\Leftrightarrow\mathrm{P}+\mathrm{Q}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{P}^{\mathrm{2}}…

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…