Category: Number Theory

Question Number 2381 by Yozzi last updated on 18/Nov/15 $$Ofthenumbers1,2,3,\dots ,6000,$$$$howmanyarenotmultiplesof2,3or5?$$ Commented by 123456 last updated on 18/Nov/15 $$\mathrm{N}=\mathrm{N}_{\mathrm{2}} +\mathrm{N}_{\mathrm{3}} +\mathrm{N}_{\mathrm{5}} −\mathrm{N}_{\mathrm{2},\mathrm{3}}…

Question Number 133320 by bramlexs22 last updated on 21/Feb/21 $$\mathrm{Find}\mathrm{all}\mathrm{n}\mathrm{for}\mathrm{which}{\mathrm{n}}^2+2\mathrm{n}+4$$$$\mathrm{is}\mathrm{divisible}\mathrm{by}7$$ Answered by EDWIN88 last updated on 21/Feb/21 $$\mathrm{let}\:\mathrm{n}\:=\:\mathrm{7k}+\mathrm{r}\:\mathrm{then}\:\mathrm{n}^{\mathrm{2}} +\mathrm{2n}+\mathrm{4}\:=\:\left(\mathrm{7k}+\mathrm{r}\right)^{\mathrm{2}} +\mathrm{2}\left(\mathrm{7k}+\mathrm{r}\right)+\mathrm{4}…

Question Number 1942 by Yozzi last updated on 25/Oct/15 $$LetNbeapositiveintegerwithprime$$$$factorisation$$$$\:\:{N}={p}_{\mathrm{1}} ^{{m}_{\mathrm{1}} } {p}_{\mathrm{2}} ^{{m}_{\mathrm{2}} } {p}_{\mathrm{3}} ^{{m}_{\mathrm{3}} } ×…×{p}_{{n}−\mathrm{1}} ^{{m}_{{n}−\mathrm{1}} }…

Question Number 1776 by 123456 last updated on 20/Sep/15 $${\mathbf{P}}_k=\{x\in \mathbb{N},n\in \mathbb{N}:x>0,\sum _{n\mid x}1=k\}$$$$\mathbf{C}=\underset{k⩾3}{\cup }{\mathbf{P}}_k$$$$\{0,1\}\cup \mathbf{C}\cup \mathbb{P}=\mathbb{N}$$$$\mathrm{proof}\mathrm{or}\mathrm{give}\mathrm{a}\mathrm{counter}\mathrm{example}\mathrm{that}$$$$(x,y,z)\in {\mathbf{C}}^3,x^2\mid yz\Rightarrow x\mid y\vee x\mid z$$…

Question Number 67193 by Rasheed.Sindhi last updated on 23/Aug/19 Commented by Rasheed.Sindhi last updated on 24/Aug/19 $$\underset{-}{\mathbb{S}\mathrm{ome}\mathbb{C}\mathrm{ounting}\mathbb{P}\mathrm{roblems}}$$$$\left(a\right)Howmanyrectanglesareinthe$$$$abovepicture?$$$$\left({b}\right){How}\:{many}\:{rectangles}\:{contain} \…