Question Number 45221 by malwaan last updated on 10/Oct/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{divisors}\:; \\ $$$$\mathrm{if}\:\mathrm{any}\:;\:\mathrm{of}\:\mathrm{16000001} \\ $$ Answered by MJS last updated on 10/Oct/18 $$\mathrm{16000001}=\mathrm{109}×\mathrm{229}×\mathrm{641} \\ $$ Commented…
Question Number 110688 by Aina Samuel Temidayo last updated on 30/Aug/20 $$\mathrm{Let}\:\mathrm{a},\mathrm{b}\:\mathrm{and}\:\mathrm{c}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{ab}+\mathrm{1}\mid\mathrm{bc}+\mathrm{1}\:\mathrm{and}\:\mathrm{bc}+\mathrm{1}\mid\mathrm{ca}+\mathrm{1}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{ab}+\mathrm{1}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two} \\ $$$$\mathrm{squares}. \\ $$ Terms of Service Privacy Policy…
Question Number 110644 by Aina Samuel Temidayo last updated on 29/Aug/20 $$\mathrm{The}\:\mathrm{Diophantine}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{1}\:=\mathrm{N}\left(\mathrm{xy}+\mathrm{1}\right)\:\mathrm{has} \\ $$$$\mathrm{infinitely}\:\mathrm{many}\:\mathrm{integer} \\ $$$$\mathrm{solutions}\:\mathrm{if}\:\mathrm{N}\:\mathrm{equals}? \\ $$$$\mathrm{Any}\:\mathrm{help}\:\mathrm{please}? \\ $$ Commented…
Question Number 110595 by Aina Samuel Temidayo last updated on 29/Aug/20 $$\mathrm{Evaluate}\:\mathrm{5}!\bullet\mathrm{6}!\left(\mathrm{mod}\:\mathrm{7}!\right) \\ $$ Commented by Her_Majesty last updated on 29/Aug/20 $${you}'{re}\:{right} \\ $$ Commented…
Question Number 110591 by Aina Samuel Temidayo last updated on 29/Aug/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{positive} \\ $$$$\mathrm{two}−\mathrm{digit}\:\mathrm{integers}\:\mathrm{that}\:\mathrm{are}\:\mathrm{divisible} \\ $$$$\mathrm{by}\:\mathrm{each}\:\mathrm{of}\:\mathrm{their}\:\mathrm{digits}. \\ $$ Answered by Rasheed.Sindhi last updated on 30/Aug/20…
Question Number 110562 by Aina Samuel Temidayo last updated on 29/Aug/20 $$\mathrm{Let}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{be}\:\mathrm{integers}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{xy}\neq\mathrm{1},\:\mathrm{x}^{\mathrm{2}} \neq\mathrm{y}\:\mathrm{and}\:\mathrm{y}^{\mathrm{2}} \neq\mathrm{x}. \\ $$$$ \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Show}\:\mathrm{that}\:\mathrm{p}\mid\mathrm{xy}−\mathrm{1}\:\mathrm{and}\:\mathrm{p}\mid\mathrm{x}^{\mathrm{2}} −\mathrm{y} \\ $$$$\mathrm{then}\:\mathrm{p}\mid\mathrm{y}^{\mathrm{2}} −\mathrm{x}\:\mathrm{where}\:\mathrm{p}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}. \\…
Question Number 110565 by Aina Samuel Temidayo last updated on 29/Aug/20 $$\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)…