Category: Number Theory

Question Number 44333 by Tawa1 last updated on 27/Sep/18 $$\mathrm{Can}\mathrm{positive}\mathrm{integers}\mathrm{a},\mathrm{b},\mathrm{c}\mathrm{be}\mathrm{found}\mathrm{such}\mathrm{that}{\mathrm{a}}^3+{\mathrm{b}}^3={\mathrm{c}}^3?$$ Commented by MrW3 last updated on 28/Sep/18 $$nobodyhasfoundsuchintegersa,b,c$$$${that}\:{a}^{{n}}…

Question Number 109729 by lazygorilla last updated on 25/Aug/20 Answered by prakash jain last updated on 25/Aug/20 $$1+x+x^2+..+x^{n-1}=\frac{(x^n-1)}{x-1}(x\ne 1)$$$$\left(\mathrm{Geometric}\mathrm{Progression}\right)$$$$\mathrm{2}^{\mathrm{0}}…

Question Number 44059 by paro123 last updated on 20/Sep/18 $$\mathrm{Prove}\mathrm{that}\mathrm{any}\mathrm{integer}\mathrm{can}\mathrm{be}\mathrm{expressed}$$$$\mathrm{as}\mathrm{in}\mathrm{the}\mathrm{form}\mathrm{of}4\mathrm{k}\mathrm{or}4\mathrm{k}\underset{-}{+}1\mathrm{or}4\mathrm{k}\underset{-}{+}2.$$ Answered by kunal1234523 last updated on 21/Sep/18 $${any}\:{integer}\:{p}\:{can}\:{be}\:{expressed}\:{in}\:{the}\:{form} \…

Question Number 174566 by RajiYusuf last updated on 04/Aug/22 Answered by aleks041103 last updated on 05/Aug/22 $$f\left(n\right)=2n-\sigma \left(n\right)$$$$\sigma \left(n\right)=\sum _{i>0,i\mid n}i$$$$\sigma \left(p^2\right)=1+p+p^2$$$$\Rightarrow{f}\left({p}^{\mathrm{2}}…

Question Number 108516 by Rasheed.Sindhi last updated on 17/Aug/20 $$\mathrm{If}\mathrm{x}+\frac{1}{\mathrm{x}}=2(\mathrm{x}\ne 0),\mathrm{prove}\mathrm{that}$$$${\mathrm{x}}^{\mathrm{n}}+\frac{1}{{\mathrm{x}}^{\mathrm{n}}}=2\mathrm{\forall }n\in \mathbb{Z}$$ Commented by mr W last updated on 17/Aug/20 $${if}\:{x}>\mathrm{0}:…