Category: Arithmetic

Question Number 79647 by john santu last updated on 27/Jan/20 $$\mathrm{discussion}\mathrm{back}\mathrm{with}\mathrm{mr}\mathrm{W}.$$$$\mathrm{consider}\mathrm{this}\mathrm{equation}$$$$({\mathrm{x}}^2-2\mathrm{x}-3)(3^{\mathrm{x}}-27)=0$$$$\mathrm{does}\mathrm{the}\mathrm{equation}\mathrm{have}\mathrm{two}\mathrm{roots}$$$$\mathrm{or}\mathrm{three}\mathrm{roots}?$$ Commented by…

Question Number 14047 by FilupS last updated on 27/May/17 $$S=1+i-1-i+1+\dots$$$$\frac{1}{i}=-i$$$$S=i(-i+1+i-1-i+1+\dots )$$$$S=i(-i+S)$$$$S=1+iS$$$$S(1-i)=1$$$$\therefore S=\frac{1}{1-i}$$$$\: \…

Question Number 13934 by tawa tawa last updated on 25/May/17 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 144980 by henderson last updated on 01/Jul/21 $$\underset{―}{\mathbf{exercise}}$$$$\mathbf{Let}\mathit{a}\mathbf{and}\mathit{b}\mathbf{be}\mathbf{natural}\mathbf{integers}\mathbf{such}\mathbf{that}0<\mathit{a}<\mathit{b}.$$$$1.\mathbf{Show}\mathbf{that}\mathbf{if}\mathit{a}\mathbf{divides}\mathit{b},\mathbf{then}\mathbf{for}\mathbf{any}\mathbf{naturel}$$$$\mathbf{number}\mathit{n},{\mathit{n}}^{\mathit{a}}-1\mathbf{divides}{\mathit{n}}^{\mathit{b}}-1.$$$$$$$$2.\mathbf{For}\mathbf{any}\mathbf{non}-\mathbf{zero}\mathbf{naturel}\mathbf{number}\mathit{n},\mathbf{prove}$$$$\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{remainder}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{euclidean}}\:\boldsymbol{\mathrm{division}}\:\boldsymbol{\mathrm{of}}\: \…

Question Number 144734 by help last updated on 28/Jun/21 Terms of Service Privacy Policy Contact: info@tinkutara.com