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Category: Number Theory

solve-for-integer-x-y-4x-2-9y-2-6-

Question Number 187 by 123456 last updated on 25/Jan/15 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{integer}\:{x},{y} \\ $$$$\mathrm{4}{x}^{\mathrm{2}} −\mathrm{9}{y}^{\mathrm{2}} =\mathrm{6} \\ $$ Answered by ghosea last updated on 16/Dec/14 $$\left(\mathrm{2}{x}−\mathrm{3}{y}\right)\left(\mathrm{2}{x}+\mathrm{3}{y}\right)=\mathrm{2}\centerdot\mathrm{3}\:{or}\:\mathrm{1}.\mathrm{6}\:{or}\:−\mathrm{1},−\mathrm{6}\:{or}−\mathrm{2},−\mathrm{3} \\…

solve-30x-50-mod-40-

Question Number 190 by 123456 last updated on 25/Jan/15 $$\mathrm{solve}\:\mathrm{30x}\equiv\mathrm{50}\left(\mathrm{mod}\:\mathrm{40}\right) \\ $$ Answered by mreddy last updated on 15/Dec/14 $$\mathrm{30}{x}+\mathrm{40}{y}=\mathrm{50} \\ $$$$\mathrm{3}{x}+\mathrm{4}{y}=\mathrm{5} \\ $$$$\mathrm{general}\:\mathrm{solution} \\…

solve-10x-25-mod-15-

Question Number 185 by 123456 last updated on 25/Jan/15 $$\mathrm{solve}\:\mathrm{10x}\equiv\mathrm{25}\left(\mathrm{mod}\:\mathrm{15}\right) \\ $$ Answered by mreddy last updated on 14/Dec/14 $$\mathrm{gcd}\left(\mathrm{10},\mathrm{15}\right)=\mathrm{5}\:\mathrm{and}\:\mathrm{5}\:\mathrm{divided}\:\mathrm{25}\:\mathrm{so}\: \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{5}\:\mathrm{solutions} \\ $$$$\mathrm{Solutions}\:\mathrm{are}\:\mathrm{given}\:\mathrm{by}\:\mathrm{equation} \\…

find-the-integer-solution-of-3x-4y-5-

Question Number 176 by 123456 last updated on 25/Jan/15 $$\mathrm{find}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{3x}+\mathrm{4y}=\mathrm{5} \\ $$ Answered by prakash jain last updated on 14/Dec/14 $$\mathrm{gcd}\left(\mathrm{3},\mathrm{4}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{1}\:\mathrm{divides}\:\mathrm{5}\:\mathrm{so}\:\mathrm{it}\:\mathrm{is}\:\mathrm{solvable}. \\ $$$$\mathrm{Particular}\:\mathrm{solution}\:{x}=\mathrm{3},\:{y}=−\mathrm{1} \\ $$$$\mathrm{General}\:\mathrm{solution}…

solve-12x-34-mod-56-

Question Number 177 by 123456 last updated on 25/Jan/15 $$\mathrm{solve}\:\mathrm{12x}\equiv\mathrm{34}\left(\mathrm{mod}\:\mathrm{56}\right) \\ $$ Answered by prakash jain last updated on 14/Dec/14 $$\mathrm{gcd}\left(\mathrm{12},\mathrm{56}\right)=\mathrm{4}\: \\ $$$$\mathrm{4}\:\mathrm{does}\:\mathrm{not}\:\mathrm{divide}\:\mathrm{34}\:\mathrm{so}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solutions}. \\ $$…

solve-12x-25-mod-69-

Question Number 170 by 123456 last updated on 25/Jan/15 $$\mathrm{solve}\:\mathrm{12x}\equiv\mathrm{25}\left(\mathrm{mod}\:\mathrm{69}\right) \\ $$ Answered by prakash jain last updated on 14/Dec/14 $$\mathrm{gcd}\left(\mathrm{12},\mathrm{69}\right)=\mathrm{3} \\ $$$$\mathrm{3}\:\nmid\:\mathrm{25},\:\mathrm{3}\:\mathrm{does}\:\mathrm{not}\:\mathrm{divide}\:\mathrm{25}\:\mathrm{hence}\:\mathrm{there} \\ $$$$\mathrm{is}\:\mathrm{no}\:\mathrm{solution}.…

express-the-folowing-in-the0-6-bar-form-of-p-q-where-p-and-q-are-integers-and-q-is-not-0-0-6-

Question Number 139 by shaleen last updated on 25/Jan/15 $$\boldsymbol{{express}}\:\boldsymbol{{the}}\:\boldsymbol{{folowing}}\:\boldsymbol{{in}}\:\boldsymbol{{the}}\mathrm{0}.\mathrm{6}\left(\boldsymbol{{bar}}\right)= \\ $$$$\boldsymbol{{form}}\:\boldsymbol{{of}}\:\boldsymbol{{p}}/\boldsymbol{{q}}\:;{where}\:{p}\:{and}\:{q} \\ $$$${are}\:{integers}\:{and}\:{q}\:{is}\:{not}\:=\mathrm{0} \\ $$$$\mathrm{0}.\bar {\mathrm{6}} \\ $$ Answered by vkulkarni last updated on…

The-minimum-value-of-the-expression-B-z-2-z-3-2-z-6i-2-is-p-What-the-value-of-p-10-

Question Number 131196 by john_santu last updated on 02/Feb/21 $$\:{The}\:{minimum}\:{value}\:{of}\:{the}\: \\ $$$${expression}\:{B}\:=\:\mid{z}\mid^{\mathrm{2}} +\mid{z}−\mathrm{3}\mid^{\mathrm{2}} +\mid{z}−\mathrm{6}{i}\mid^{\mathrm{2}} \\ $$$${is}\:{p}.\:{What}\:{the}\:{value}\:{of}\:\frac{{p}}{\mathrm{10}}\:.? \\ $$ Answered by liberty last updated on 02/Feb/21…

Let-R-be-a-cummutative-ring-with-1-and-a-b-member-of-R-Suppose-a-is-invertible-and-b-is-nilpotent-Show-that-a-b-is-invertible-

Question Number 12843 by tawa last updated on 04/May/17 $$\mathrm{Let}\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{cummutative}\:\mathrm{ring}\:\mathrm{with}\:\mathrm{1}.\:\mathrm{and}\:\mathrm{a},\mathrm{b}\:\:\mathrm{member}\:\mathrm{of}\:\mathrm{R}.\:\mathrm{Suppose}\:\mathrm{a}\:\mathrm{is} \\ $$$$\mathrm{invertible}\:\mathrm{and}\:\mathrm{b}\:\mathrm{is}\:\mathrm{nilpotent}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{a}\:+\:\mathrm{b}\:\mathrm{is}\:\mathrm{invertible}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com