Category: Arithmetic

Question Number 85857 by M±th+et£s last updated on 25/Mar/20 Answered by mind is power last updated on 26/Mar/20 $$n^2=\frac{1}{4}({(2n-1)}^2+2(2n-1)+1))$$$$\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}}…

Question Number 20235 by naziri1920@gmail.com last updated on 24/Aug/17 $$$$$$if{t}_{(m+1)}=2t_{(n+1)}$$$$soproof$$$$t_{(3m+1)}=2t_{(m+n+1)}$$$$helpplease\dots \dots \dots$$$$$$$$ \…

Question Number 151256 by pticantor last updated on 19/Aug/21 $$A_n=2^n+3^n+4^n+5^n$$$$B_n={100}^n+{101}^n+{102}^n+{103}^n$$$$1)\mathit{f}\mathit{i}\mathit{n}\mathit{d}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathit{s}\mathit{o}\mathit{f}\mathit{n}\mathit{w}\mathit{h}\mathit{i}\mathit{l}\mathit{e}7\mid {\mathit{A}}_{\mathit{n}}$$$$\left.\mathrm{2}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{B}}_{\boldsymbol{{n}}} \equiv\boldsymbol{{A}}_{\boldsymbol{{n}}}…

Question Number 85588 by TawaTawa1 last updated on 23/Mar/20 Commented by john santu last updated on 23/Mar/20 $$14,450=\frac{a(4^n-1)}{3}$$$$43,350=a(4^n-1)$$$${a}\:=\:\frac{\mathrm{43},\mathrm{350}}{\mathrm{4}^{{n}} −\mathrm{1}}\:\Rightarrow\:\mathrm{100}<\frac{\mathrm{43},\mathrm{350}}{\mathrm{4}^{{n}}…

Question Number 151079 by mathdanisur last updated on 18/Aug/21 Answered by dumitrel last updated on 18/Aug/21 Commented by dumitrel last updated on 18/Aug/21 Commented by…