Question Number 110354 by Aina Samuel Temidayo last updated on 28/Aug/20 $$\mathrm{The}\:\mathrm{Diophantine}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{1}\:=\mathrm{N}\left(\mathrm{xy}+\mathrm{1}\right)\:\mathrm{has} \\ $$$$\mathrm{infinitely}\:\mathrm{many}\:\mathrm{integer} \\ $$$$\mathrm{solutions}\:\mathrm{if}\:\mathrm{N}\:\mathrm{equals}? \\ $$ Commented by Aina…
Question Number 175799 by cortano1 last updated on 07/Sep/22 $$\:\:\mathrm{For}\:\mathrm{x}\:,\mathrm{y}\:\varepsilon\:\mathbb{Z}^{+} \:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\:\mathrm{7x}+\mathrm{9y}=\mathrm{405}.\:\mathrm{Find}\:\mathrm{max}\:\mathrm{value} \\ $$$$\:\:\mathrm{of}\:\mathrm{x}−\mathrm{y}. \\ $$ Answered by mr W last updated on 07/Sep/22…
Question Number 44716 by Tawa1 last updated on 03/Oct/18 $$\mathrm{prove}:\:\:\:\:\:\mathrm{1}\:+\:\mathrm{11}\:+\:\mathrm{111}\:+\:….\:+\:\frac{\mathrm{111}\:…\mathrm{111}}{\mathrm{n}\:\mathrm{times}}\:\:=\:\:\frac{\mathrm{10}^{\mathrm{n}\:+\:\mathrm{1}} \:−\:\mathrm{9n}\:−\:\mathrm{10}}{\mathrm{81}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 03/Oct/18 $${s}=\mathrm{1}+\mathrm{11}+\mathrm{111}+\mathrm{1111}+…+\mathrm{111}..\underset{{n}\:{times}} {.}\mathrm{111} \\ $$$$\mathrm{9}{s}=\mathrm{9}+\mathrm{99}+\mathrm{999}+\mathrm{9999}+…+\mathrm{999}…\mathrm{999} \\…
Question Number 44704 by Tawa1 last updated on 03/Oct/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\::\:\:\:\:\:\:\:\:\:\:\:\mathrm{311x}\:−\:\mathrm{112y}\:=\:\mathrm{73} \\ $$ Answered by Joel578 last updated on 04/Oct/18 $$\mathrm{311}{x}\:−\:\mathrm{112}{y}\:=\:\mathrm{73} \\ $$$$\mathrm{311}{x}\:=\:\mathrm{73}\:+\:\mathrm{112}{y} \\ $$$${x}\:=\:\frac{\mathrm{73}}{\mathrm{311}}\:+\:\frac{\mathrm{112}}{\mathrm{311}}{y} \\…
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Question Number 44333 by Tawa1 last updated on 27/Sep/18 $$\mathrm{Can}\:\mathrm{positive}\:\mathrm{integers}\:\:\mathrm{a},\:\mathrm{b},\:\mathrm{c}\:\:\mathrm{be}\:\mathrm{found}\:\mathrm{such}\:\mathrm{that}\:\:\:\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:=\:\mathrm{c}^{\mathrm{3}\:\:\:} ? \\ $$ Commented by MrW3 last updated on 28/Sep/18 $${nobody}\:{has}\:{found}\:{such}\:{integers}\:{a},{b},{c} \\ $$$${that}\:{a}^{{n}}…
Question Number 175320 by cortano1 last updated on 27/Aug/22 $$\:\:\begin{cases}{\mathrm{4}{x}=\mathrm{2}\left({mod}\:\mathrm{9}\right)}\\{\mathrm{7}{x}=\mathrm{2}\:\left({mod}\:\mathrm{13}\right)}\end{cases} \\ $$ Commented by cortano1 last updated on 27/Aug/22 $${i}\:{got}\:{x}=\mathrm{23}\:+\mathrm{117}{k}\:{sir} \\ $$ Commented by Rasheed.Sindhi…
Question Number 109729 by lazygorilla last updated on 25/Aug/20 Answered by prakash jain last updated on 25/Aug/20 $$\mathrm{1}+{x}+{x}^{\mathrm{2}} +..+{x}^{{n}−\mathrm{1}} =\frac{\left({x}^{{n}} −\mathrm{1}\right)}{{x}−\mathrm{1}}\:\:\:\left({x}\neq\mathrm{1}\right) \\ $$$$\:\:\:\:\left(\mathrm{Geometric}\:\mathrm{Progression}\right) \\ $$$$\mathrm{2}^{\mathrm{0}}…
Question Number 175221 by kaivan.ahmadi last updated on 23/Aug/22 Answered by a.lgnaoui last updated on 23/Aug/22 $$\left(\mathrm{2}+\mathrm{1}\right)×\mathrm{6}×\mathrm{6} \\ $$ Answered by JDamian last updated on…
Question Number 44059 by paro123 last updated on 20/Sep/18 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{any}\:\mathrm{integer}\:\mathrm{can}\:\mathrm{be}\:\mathrm{expressed}\: \\ $$$$\mathrm{as}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\mathrm{of}\:\mathrm{4k}\:\mathrm{or4k}\underset{−} {+}\mathrm{1}\:\mathrm{or}\:\mathrm{4k}\underset{−} {+}\mathrm{2}. \\ $$ Answered by kunal1234523 last updated on 21/Sep/18 $${any}\:{integer}\:{p}\:{can}\:{be}\:{expressed}\:{in}\:{the}\:{form} \\…