Category: Number Theory

Question Number 126666 by bramlexs22 last updated on 23/Dec/20 $$3+33+333+3333+\dots +\underset{2020times}{\underbrace{3333\dots 3}}$$$$divideby2.findtheremainder$$ Answered by JDamian last updated on 23/Dec/20 $$itiseasy$$$$\mathrm{0}…

Question Number 191889 by cortano12 last updated on 03/May/23 $$\underset{\mathrm{n}=1}{\sum ^{\mathrm{k}}}\frac{1}{{\mathrm{n}}^2+2\mathrm{n}}=?$$ Answered by mahdipoor last updated on 03/May/23 $$\underset{{n}=\mathrm{1}} {\overset{{k}} {\sum}}\:\frac{\mathrm{1}}{{n}^{\mathrm{2}}…

Question Number 191846 by malwan last updated on 01/May/23 $$findthelastthreedigits$$$$of{4}^{2^{42}}$$$$MohammedAlwan$$ Answered by AST last updated on 01/May/23 $$\mathrm{4}^{\mathrm{2}^{\mathrm{42}}…

Question Number 191710 by pete last updated on 29/Apr/23 $$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{remainder}\mathrm{f}149!\mathrm{when}\mathrm{divided}$$$$\mathrm{by}139?$$ Commented by Rasheed.Sindhi last updated on 29/Apr/23 $$149!=1.2.3\dots 138.139.140\dots 148.149$$$$\therefore\:\mathrm{149}!\mathrm{mod139}=\mathrm{0} \…

Question Number 125959 by bramlexs22 last updated on 15/Dec/20 Answered by liberty last updated on 15/Dec/20 $$Letqdenotethenumbersofeggsoriginally$$$$inthebasket.Wewanttofindtheleastnumber$$$$ofeggsinthebasket.$$$$\iff q\equiv 1\left(mod2\right)\equiv 1\left(mod3\right)\equiv 1\left(mod5\right)\equiv 0\left(mod7\right)$$$${the}\:{first}\:{three}\:{congruences}\:{then}…