Category: Number Theory

Question Number 96558 by bobhans last updated on 02/Jun/20 $$\mathrm{Let}\mathrm{m}\mathrm{and}\mathrm{n}\mathrm{be}\mathrm{two}\mathrm{positive}\mathrm{integers}$$$$\mathrm{satisfy}\frac{\mathrm{m}}{\mathrm{n}}=\frac{1}{10\times 12}+\frac{1}{12\times 14}+\frac{1}{14\times 16}+\dots +\frac{1}{2012\times 2014}$$$$\mathrm{find}\mathrm{the}\mathrm{smallest}\mathrm{possible}\mathrm{value}\mathrm{of}$$$$\mathrm{m}+\mathrm{n}$$ Answered by john santu last updated on…

Question Number 30897 by usman katyar last updated on 28/Feb/18 $$(44x+28y)2$$ Commented by rahul 19 last updated on 28/Feb/18 $$?$$$$\mathrm{88}{x}+\mathrm{56}{y}\:. \…

Question Number 161843 by Rasheed.Sindhi last updated on 23/Dec/21 $$\text{You can't use 'macro parameter character \#' in math mode}$$$$\mathrm{Solve}\mathrm{for}\mathbf{integer}\mathrm{numbers}:$$$$\frac{\mathrm{x}}{\mathrm{y}}+\frac{5}{\mathrm{x}}+\frac{\mathrm{y}-5}{5}=\frac{\mathrm{y}+\mathrm{x}}{\mathrm{y}+5}+\frac{5+\mathrm{y}}{5+\mathrm{x}}$$ Commented by malwan last updated on 23/Dec/21 $${x}=\mathrm{0}\:{or}\:{x}=\mathrm{5} \…

Question Number 161622 by amin96 last updated on 20/Dec/21 $$\underset{\mathit{n}=1}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^{\mathit{n}+1}}{\mathit{n}(2\mathit{n}+1)}=?$$ Answered by mathmax by abdo last updated on 20/Dec/21 $$\frac{\mathrm{S}}{\mathrm{2}}=−\sum_{\mathrm{n}=\mathrm{1}}…

Question Number 95966 by i jagooll last updated on 29/May/20 $$\mathrm{find}\mathrm{all}\mathrm{pairs}\mathrm{of}\mathrm{integer}\mathrm{for}$$$$\mathrm{xy}+3\mathrm{x}-4\mathrm{y}=29$$ Answered by john santu last updated on 29/May/20 $$\Rightarrow\mathrm{3}{x}+{xy}−\mathrm{4}{y}−\mathrm{12}\:=\:\mathrm{17}\: \…