Category: Number Theory

Question Number 95768 by john santu last updated on 27/May/20 $$\mathrm{find}\mathrm{x}\mathrm{such}\mathrm{that}$$$$x\equiv 3\left(\mathrm{mod}5\right)$$$$x\equiv 5\left(\mathrm{mod}7\right)$$$$x\equiv 7\left(\mathrm{mod}11\right)$$ Commented by PRITHWISH SEN 2 last…

Question Number 30032 by Penguin last updated on 15/Feb/18 $${(x+1)}^x-x^{(x+1)}=1$$$$x=?$$ Commented by Penguin last updated on 15/Feb/18 $$\mathrm{x}=\mathrm{2}\:{works} \…

Question Number 160270 by alf123 last updated on 27/Nov/21 Answered by Rasheed.Sindhi last updated on 27/Nov/21 $$(x^2+y)(y^2+x)={(x-y)}^3$$$$\Rightarrow\begin{cases}{\underset{\left({i}\right)} {\underbrace{{x}^{\mathrm{2}} +{y}={x}−{y}}}\:\wedge\underset{\left({ii}\right)} {\underbrace{\:{y}^{\mathrm{2}} +{x}=\left({x}−{y}\right)^{\mathrm{2}}…

Question Number 160061 by Rasheed.Sindhi last updated on 24/Nov/21 $$$$$$Findoutsomepairs(a,b)suchthat$$$$forsomen⩾1$$$${a}^{{n}} +{b}^{{n}} ,{a}^{\mathrm{2}{n}} +{b}^{\mathrm{2}{n}} ,{a}^{\mathrm{4}{n}} +{b}^{\mathrm{4}{n}} ,{a}^{\mathrm{8}{n}} +{b}^{\mathrm{8}{n}} \in\mathbb{P} \…

Question Number 159775 by Ghaniy last updated on 22/Nov/21 $$\prod _{\mathrm{n}=1}^{\mathrm{\infty }}\frac{{\alpha }^3+{\beta }^2}{3^{\mathrm{n}}}=?$$$$\mathrm{in}\mathrm{expanded}\mathrm{form}$$ Answered by Canebulok last updated on…