Category: Number Theory

Question Number 400 by 123456 last updated on 25/Jan/15 $$\frac{1}{3^{20}}\mathrm{have}\mathrm{how}\mathrm{many}\mathrm{digits}\mathrm{in}\mathrm{periodic}\mathrm{part}?$$ Answered by prakash jain last updated on 29/Dec/14 $$3^{20}\mathrm{is}\mathrm{not}\mathrm{divisible}\mathrm{by}2\mathrm{or}5.\mathrm{So}$$$$\mathrm{periodicity}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\mathrm{equation}…

Question Number 348 by 123456 last updated on 23/Dec/14 $$a_n=1-\frac{2}{3-\frac{4}{5-n}},n\equiv 1\left(\mathrm{mod}2\right)$$$$a_n=1-\frac{2}{3-\frac{4}{5-\frac{6}{n}}},n\equiv 0\left(\mathrm{mod}2\right)$$$$\underset{n\to \mathrm{\infty }}{\lim }{a}_n\stackrel{?}{=}1$$ Commented by 123456 last…

Question Number 187 by 123456 last updated on 25/Jan/15 $$\mathrm{solve}\mathrm{for}\mathrm{integer}x,y$$$$4x^2-9y^2=6$$ Answered by ghosea last updated on 16/Dec/14 $$\left(\mathrm{2}{x}−\mathrm{3}{y}\right)\left(\mathrm{2}{x}+\mathrm{3}{y}\right)=\mathrm{2}\centerdot\mathrm{3}\:{or}\:\mathrm{1}.\mathrm{6}\:{or}\:−\mathrm{1},−\mathrm{6}\:{or}−\mathrm{2},−\mathrm{3} \…

Question Number 185 by 123456 last updated on 25/Jan/15 $$\mathrm{solve}10\mathrm{x}\equiv 25\left(\mathrm{mod}15\right)$$ Answered by mreddy last updated on 14/Dec/14 $$\gcd (10,15)=5\mathrm{and}5\mathrm{divided}25\mathrm{so}$$$$\mathrm{there}\mathrm{are}5\mathrm{solutions}$$$$\mathrm{Solutions}\:\mathrm{are}\:\mathrm{given}\:\mathrm{by}\:\mathrm{equation} \…

Question Number 177 by 123456 last updated on 25/Jan/15 $$\mathrm{solve}12\mathrm{x}\equiv 34\left(\mathrm{mod}56\right)$$ Answered by prakash jain last updated on 14/Dec/14 $$\gcd (12,56)=4$$$$4\mathrm{does}\mathrm{not}\mathrm{divide}34\mathrm{so}\mathrm{the}\mathrm{equation}\mathrm{has}\mathrm{no}\mathrm{solutions}.$$…