Category: Arithmetic

Question Number 21154 by youssoufab last updated on 14/Sep/17 $$prove:\mathrm{\forall }n\in {\mathbb{N}}^{\ast },\mathrm{\forall }(a,b)\in {\mathbb{C}}^2,a^{2n+1}+b^{2n+1}=$$$$\underset{k=o}{\sum ^{2n}}{(-1)}^k{a}^k{b}^{2n-k}$$ Commented by alex041103…

Question Number 152139 by Ar Brandon last updated on 26/Aug/21 $$\mathrm{How}\mathrm{many}\mathrm{numbers}x\mathrm{are}\mathrm{found}\mathrm{between}9000\mathrm{and}11000$$$$\mathrm{and}\mathrm{verify}x=12\left[19\right],x=5\left[13\right],x=9\left[11\right]?$$ Commented by Rasheed.Sindhi last updated on 26/Aug/21 $$\mathrm{One}(x=10899)$$…

Question Number 86592 by M±th+et£s last updated on 29/Mar/20 $$provethat$$$$2\underset{x=1}{\sum ^{\mathrm{\infty }}}\frac{2^x{(x!)}^2}{\left(2x\right)!\left(x\right)}$$ Commented by M±th+et£s last updated on 29/Mar/20…

Question Number 20907 by DKumar last updated on 07/Sep/17 $$Howmanyzeroes\left(0\right)therein1\times 2\times 3\times 4\dots \dots \dots .99\times 100$$ Answered by dioph last updated on 07/Sep/17 $$\mathrm{zeros}\mathrm{in}\mathrm{number}=\mathrm{maximum}\mathrm{integer}$$$${n}\:\mathrm{such}\:\mathrm{that}\:\mathrm{10}^{{n}} =\mathrm{2}^{{n}} \mathrm{5}^{{n}} \:\mathrm{divides}\:\mathrm{the}\:\mathrm{number}.…

Question Number 20810 by Tinkutara last updated on 03/Sep/17 $$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{triples}(a,b,c)\mathrm{of}$$$$\mathrm{positive}\mathrm{integers}\mathrm{such}\mathrm{that}$$$$\left(\mathrm{i}\right)a<b<c<10\mathrm{and}\left(\mathrm{ii}\right)a,b,c,10\mathrm{form}$$$$\mathrm{the}\mathrm{sides}\mathrm{of}\mathrm{a}\mathrm{quadrilateral}?$$ Commented by Tinkutara last updated on 04/Sep/17…