Category: Algebra

Question Number 145198 by loveineq last updated on 03/Jul/21 $$\mathrm{Let}a⩾b⩾c⩾0,c^3+{(a+b)}^3\ne 0\mathrm{and}{a}^2+b^2+c^2=3.\mathrm{Prove}\mathrm{that}$$$$\frac{1}{2}⩽\frac{a^3+{(b+c)}^3+b^3+{(c+a)}^3}{c^3+{(a+b)}^3}⩽2$$$$\mathrm{Determine}\:\mathrm{when}\:\mathrm{equality}\:\mathrm{holds}.…

Question Number 14119 by RasheedSindhi last updated on 28/May/17 $$\mathrm{For}\mathrm{what}\mathrm{values}\mathrm{of}\mathrm{n}\in \mathbb{N},$$$${\omega }^{1/\mathrm{n}}\mathrm{can}\mathrm{be}\mathrm{expressed}\mathrm{as}{\omega }^{\mathrm{m}}$$$$\mathrm{where}\mathrm{m}\in \mathbb{Z}?$$ Commented by prakash jain last updated on 28/May/17…

Question Number 145187 by mathdanisur last updated on 03/Jul/21 $${(\sqrt[3]{3}+\sqrt[5]{5})}^{120}$$$$Howmanysingleunitsarethereat$$$$theopeningofthebinomial$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 14109 by FilupS last updated on 28/May/17 $$(a^p-a)\mathrm{mod}p=0$$$$\mathrm{when}\mathrm{is}\mathrm{this}\mathrm{true}?$$$$a,p\in \mathbb{Z}$$ Commented by ajfour last updated on 28/May/17 $${a}={p}\:\:\:\:\:{or}\:{just}…

Question Number 79635 by TawaTawa last updated on 26/Jan/20 $$\mathrm{Sum}:\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\dots +\frac{1}{1+2+3+\dots +8016}$$ Commented by mr W last updated on 26/Jan/20 $$=\underset{k=1}{\sum ^n}\frac{1}{1+2+3+\dots +k}$$$$=\mathrm{2}\underset{{k}=\mathrm{1}}…