Category: Number Theory

Question Number 97709 by prakash jain last updated on 09/Jun/20 Commented by prakash jain last updated on 09/Jun/20 $$\mathrm{Question}\mathrm{disappeared}\mathrm{while}\mathrm{typing}$$$$\mathrm{answer}$$$$\mathrm{Question}\mathrm{was}$$$$\mathrm{solve}\:\mathrm{2}^{{n}}…

Question Number 97576 by Rio Michael last updated on 08/Jun/20 $$\mathrm{Show}\mathrm{that}RE\left[\frac{1}{1-z}\right]=\frac{1}{2}\mathrm{where}z=\cos \theta +i\sin \theta$$$$$$ Answered by smridha last updated on 08/Jun/20 $$\boldsymbol{{RE}}\left[\frac{\mathrm{1}}{\mathrm{1}−\boldsymbol{{e}}^{\boldsymbol{{i}\theta}} }\right]=\boldsymbol{{RE}}\left[\frac{\mathrm{1}+{e}^{{i}\boldsymbol{\theta}} }{\mathrm{1}−{e}^{\mathrm{2}{i}\boldsymbol{\theta}}…

Question Number 31719 by Penguin last updated on 13/Mar/18 Commented by Penguin last updated on 13/Mar/18 Commented by Penguin last updated on 13/Mar/18 Commented by…

Question Number 31579 by Joel578 last updated on 10/Mar/18 $$\mathrm{Let}a\mathrm{and}b\mathrm{be}\mathrm{an}\mathrm{integer}\mathrm{part}\mathrm{and}\mathrm{a}\mathrm{decimal}$$$$\mathrm{fraction}\mathrm{of}\sqrt{7},\mathrm{respectively}.\mathrm{Then}\mathrm{the}\mathrm{integer}$$$$\mathrm{part}\mathrm{of}\frac{a}{b}\mathrm{is}?$$ Answered by Tinkutara last updated on 10/Mar/18 $${a}=\mathrm{2} \…

Question Number 31125 by Joel578 last updated on 02/Mar/18 $$\mathrm{Let}n\mathrm{be}\mathrm{a}\mathrm{positive}\mathrm{integer}.\mathrm{Then}{x}^2+1$$$$\mathrm{is}\mathrm{a}\mathrm{factor}\mathrm{of}{(x^4+3)}^n-{\left[(x^2+3)(x^2-1)\right]}^n$$$$\mathrm{for}\dots$$$$\left(\mathrm{A}\right)\mathrm{All}n$$$$\left(\mathrm{B}\right)\mathrm{Odd}n$$$$\left(\mathrm{C}\right)\:\mathrm{Even}\:{n}…