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Category: Number Theory

Find-all-integer-solutions-of-3-m-2n-2-1-I-only-found-m-1-2-5-by-computer-from-m-1-to-m-30000-Is-there-any-greater-solutions-

Question Number 216538 by CrispyXYZ last updated on 10/Feb/25 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{integer}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\mathrm{3}^{{m}} =\mathrm{2}{n}^{\mathrm{2}} +\mathrm{1}. \\ $$$$ \\ $$$${I}\:{only}\:{found}\:{m}=\mathrm{1},\:\mathrm{2},\:\mathrm{5}\:{by}\:{computer} \\ $$$${from}\:{m}=\mathrm{1}\:{to}\:{m}=\mathrm{30000}. \\ $$$${Is}\:{there}\:{any}\:{greater}\:{solutions}? \\ $$ Commented…

Given-a-b-c-is-natural-numbers-such-that-a-b-b-c-c-a-a-b-c-find-min-value-of-a-b-c-

Question Number 213663 by efronzo1 last updated on 13/Nov/24 $$\:\:\mathrm{Given}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{is}\:\mathrm{natural}\:\mathrm{numbers} \\ $$$$\:\:\mathrm{such}\:\mathrm{that}\:\left(\mathrm{a}−\mathrm{b}\right)\left(\mathrm{b}−\mathrm{c}\right)\left(\mathrm{c}−\mathrm{a}\right)=\mathrm{a}+\mathrm{b}+\mathrm{c}. \\ $$$$\:\:\mathrm{find}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}+\mathrm{b}+\mathrm{c}\: \\ $$ Answered by Ghisom last updated on 13/Nov/24 $$\mathrm{let}\:{a}<{b}<{c}\:\left(\:_{{c}<{a}<{b}\:\mathrm{possible}} ^{\mathrm{also}\:{b}<{c}<{a}\:\mathrm{or}}…

Find-the-number-of-non-zero-integer-solution-x-y-to-the-equation-15-x-2-y-3-xy-2-x-2-

Question Number 212999 by golsendro last updated on 28/Oct/24 $$\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{non}\:\mathrm{zero}\:\mathrm{integer}\: \\ $$$$\:\mathrm{solution}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{to}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\:\:\:\:\frac{\mathrm{15}}{\mathrm{x}^{\mathrm{2}} \mathrm{y}}\:+\:\frac{\mathrm{3}}{\mathrm{xy}}\:−\:\frac{\mathrm{2}}{\mathrm{x}}\:=\:\mathrm{2}\: \\ $$ Answered by A5T last updated on 28/Oct/24 $$\frac{\mathrm{3}−\mathrm{2}{y}}{{xy}}=\mathrm{2}−\frac{\mathrm{15}}{{x}^{\mathrm{2}}…

If-positive-integer-x-y-gt-1-gcd-x-y-1-Positive-integer-n-satisfies-that-there-is-nononnegative-integer-a-and-b-makes-n-ax-by-If-true-what-is-the-maximum-n-

Question Number 212890 by MrGaster last updated on 26/Oct/24 $$\mathrm{If}\:\mathrm{positive}\:\mathrm{integer}\:{x}+,{y}>\mathrm{1},{gcd}\left({x},{y}\right)=\mathrm{1}, \\ $$$$\mathrm{Positive}\:\mathrm{integer}\:\mathrm{n}\:\mathrm{satisfies}\:\mathrm{that}\:\mathrm{there}\:\mathrm{is}\: \\ $$$$\mathrm{nononnegative}\:\mathrm{integer}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{makes}\:\mathrm{n}={ax}+{by}\: \\ $$$$\mathrm{If}\:\mathrm{true}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{n} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com