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Category: Number Theory

How-do-you-solve-the-diophantine-equation-1-3xy-2x-y-12-2-x-3-4y-2-4y-3-

Question Number 136792 by EDWIN88 last updated on 26/Mar/21 $$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{diophantine}\:\mathrm{equation} \\ $$$$\left(\mathrm{1}\right)\mathrm{3xy}\:+\mathrm{2x}\:+\mathrm{y}\:=\:\mathrm{12}\:? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{x}^{\mathrm{3}} =\:\mathrm{4y}^{\mathrm{2}} +\mathrm{4y}−\mathrm{3}\:? \\ $$ Answered by mindispower last updated on 26/Mar/21…

Let-p-j-represent-the-j-th-prime-number-Now-define-the-number-n-whose-decimal-representation-is-written-out-in-terms-of-p-j-j-N-in-the-following-way-n-0-p-1-p-2-p-3-p-4-p-5-p-j-p-j-1-p-j-

Question Number 5216 by Yozzii last updated on 01/May/16 $${Let}\:{p}_{{j}} \:{represent}\:{the}\:{j}−{th}\:{prime}\:{number}. \\ $$$${Now},\:{define}\:{the}\:{number}\:{n}\:{whose} \\ $$$${decimal}\:{representation}\:{is}\:{written}\:{out} \\ $$$${in}\:{terms}\:{of}\:{p}_{{j}} \:\left({j}\in\mathbb{N}\right)\:{in}\:{the}\:{following} \\ $$$${way}: \\ $$$${n}=\mathrm{0}.{p}_{\mathrm{1}} {p}_{\mathrm{2}} {p}_{\mathrm{3}} {p}_{\mathrm{4}}…

Find-the-value-of-2023-mod-2027-

Question Number 5168 by Yozzii last updated on 24/Apr/16 $${Find}\:{the}\:{value}\:{of}\:\mathrm{2023}!\:\left({mod}\:\mathrm{2027}\right). \\ $$ Commented by prakash jain last updated on 27/Apr/16 $$\mathrm{If}\:\mathrm{you}\:\mathrm{find}\:\mathrm{an}\:\mathrm{answer},\:\mathrm{please}\:\mathrm{do}\:\mathrm{post}\:\mathrm{it}.\:\mathrm{I} \\ $$$$\mathrm{have}\:\mathrm{not}\:\mathrm{yet}\:\mathrm{been}\:\mathrm{able}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{it}. \\ $$…

why-1-1-2-1-4-1-8-2-

Question Number 5158 by 1771727373 last updated on 24/Apr/16 $${why} \\ $$$$\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\:+\:\frac{\mathrm{1}}{\mathrm{8}}\:+\:………..\:=\:\mathrm{2} \\ $$$$ \\ $$ Answered by FilupSmith last updated on 24/Apr/16 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}+…={S} \\…

Let-n-j-q-Z-1-Are-there-triples-n-j-q-such-that-the-following-conditions-are-satisfied-altogether-i-n-j-q-ii-n-2-j-2-q-2-Suppose-then-that-condition-ii-

Question Number 5144 by Yozzii last updated on 19/Apr/16 $${Let}\:{n},{j},{q}\in\left(\mathbb{Z}^{+} −\left\{\mathrm{1}\right\}\right).\:{Are}\:{there}\: \\ $$$${triples}\:\left({n},{j},{q}\right)\:{such}\:{that}\:{the}\:{following} \\ $$$${conditions}\:{are}\:{satisfied}\:{altogether}? \\ $$$$\left({i}\right)\:{n}={j}^{{q}} \:\:\:\: \\ $$$$\left({ii}\right){n}^{\mathrm{2}} ={j}^{\mathrm{2}} +{q}^{\mathrm{2}} \\ $$$$−−−−−−−−−−−−−−−−−−−−−− \\…