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Category: Number Theory

Given-that-p-q-are-primes-and-pq-divides-p-2-q-2-4-How-many-possible-values-does-p-q-have-

Question Number 110357 by Aina Samuel Temidayo last updated on 28/Aug/20 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{p},\mathrm{q}\:\mathrm{are}\:\mathrm{primes}\:\mathrm{and}\:\mathrm{pq} \\ $$$$\mathrm{divides}\:\mathrm{p}^{\mathrm{2}} +\mathrm{q}^{\mathrm{2}} −\mathrm{4}.\:\mathrm{How}\:\mathrm{many} \\ $$$$\mathrm{possible}\:\mathrm{values}\:\mathrm{does}\:\mid\mathrm{p}−\mathrm{q}\mid\:\mathrm{have}? \\ $$ Commented by Aina Samuel Temidayo…

The-Diophantine-equation-x-2-y-2-1-N-xy-1-has-infinitely-many-integer-solutions-if-N-equals-

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…

prove-1-11-111-111-111-n-times-10-n-1-9n-10-81-

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} \\…

Find-the-general-solution-of-311x-112y-73-

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} \\…

Can-positive-integers-a-b-c-be-found-such-that-a-3-b-3-c-3-

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}}…

4x-2-mod-9-7x-2-mod-13-

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-109729

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}}…