Question Number 110565 by Aina Samuel Temidayo last updated on 29/Aug/20 $$\mathrm{Let}\:\mathrm{n}\in\mathbb{N}.\:\mathrm{Using}\:\mathrm{the}\:\mathrm{formula}\:\mathrm{lcm}\left(\mathrm{a},\mathrm{b}\right) \\ $$$$=\:\frac{\mathrm{ab}}{\mathrm{gcd}\left(\mathrm{a},\mathrm{b}\right)}\:\mathrm{and}\:\mathrm{lcm}\left(\mathrm{a},\mathrm{b},\mathrm{c}\right) \\ $$$$=\mathrm{lcm}\left(\mathrm{lcm}\left(\mathrm{a},\mathrm{b}\right),\mathrm{c}\right),\:\mathrm{find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{possible} \\ $$$$\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{6}\bullet\mathrm{lcm}\left(\mathrm{n},\mathrm{n}+\mathrm{1},\mathrm{n}+\mathrm{2},\mathrm{n}+\mathrm{3}\right)}{\mathrm{n}\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{2}\right)\left(\mathrm{n}+\mathrm{3}\right)} \\ $$ Commented by kaivan.ahmadi last updated…
Question Number 44986 by Tawa1 last updated on 07/Oct/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{5}.\mathrm{6}}\:+\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{8}.\mathrm{9}}\:+\:… \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 07/Oct/18 $${pls}\:{write}\:{the}\:{answer}\:{of}\:{questiins}\:{snd}\:{source}\:{of}\: \\ $$$${question}… \\ $$ Answered…
Question Number 110519 by bobhans last updated on 29/Aug/20 $$\:\:\:\:\:\:\mathrm{17x}\:\equiv\:\mathrm{3}\:\left(\mathrm{mod}\:\mathrm{29}\right) \\ $$ Commented by kaivan.ahmadi last updated on 29/Aug/20 $$\mathrm{17}{x}\overset{\mathrm{29}} {\equiv}\mathrm{3}\Rightarrow\mathrm{34}{x}\overset{\mathrm{29}} {\equiv}\mathrm{6}\Rightarrow\mathrm{5}{x}\overset{\mathrm{29}} {\equiv}\mathrm{6}\Rightarrow\mathrm{30}{x}\overset{\mathrm{29}} {\equiv}\mathrm{36}\Rightarrow \\…
Question Number 110358 by bobhans last updated on 28/Aug/20 $${if}\:{positive}\:{integer}\:{x}\:{satisfies}\:{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{56}\:\equiv\mathrm{14}\:\left({mod}\:\mathrm{17}\right)\: \\ $$$$,\:{what}\:{is}\:{the}\:{minimum}\:{value}\:{of}\:{x}. \\ $$ Answered by john santu last updated on 28/Aug/20 $$\Leftrightarrow{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{4}\:+\:\mathrm{52}\:=\:\mathrm{14}\:\left({mod}\:\mathrm{17}\right)…
Question Number 110357 by Aina Samuel Temidayo last updated on 28/Aug/20 $$\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…
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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