Category: Number Theory

Question Number 182199 by depressiveshrek last updated on 05/Dec/22 $$LetS=\{1,2,3,4,5,6,7\}$$$$Ifwemultiplyatleast2numbers$$$$fromthissetwitheachother,what$$$$arethechancesoftheproductto$$$$turnouttobedivisibleby3?$$ Answered by Acem last updated…

Question Number 116356 by bemath last updated on 03/Oct/20 $$\mathrm{Let}\mathrm{S}=\{1,2,3,4,\dots ,48,49\}.\mathrm{What}\mathrm{is}$$$$\mathrm{the}\mathrm{maximum}\mathrm{value}\mathrm{of}\mathrm{n}\mathrm{such}\mathrm{that}$$$$\mathrm{it}\mathrm{is}\mathrm{possible}\mathrm{to}\mathrm{select}\mathrm{n}\mathrm{numbers}$$$$\mathrm{from}\mathrm{S}\mathrm{and}\mathrm{arrange}\mathrm{them}\mathrm{in}\mathrm{a}\mathrm{circle}$$$$\mathrm{in}\mathrm{such}\mathrm{a}\mathrm{way}\mathrm{that}\mathrm{the}\mathrm{product}\mathrm{of}$$$$\mathrm{any}\mathrm{two}\mathrm{adjacent}\mathrm{numbers}\mathrm{in}\mathrm{the}$$$$\mathrm{circle}\mathrm{is}\mathrm{less}\mathrm{than}100?$$ Terms…

Question Number 115742 by bemath last updated on 28/Sep/20 $$whatthecooefficientof{x}^{10}from$$$$(1+x)\times (1+2x^2)\times (1+3x^3)\times \dots \times (1+2020x^{2020})$$ Answered by mr W last updated on…

Question Number 180776 by Acem last updated on 17/Nov/22 $$Simplify\sqrt{\frac{4}{\sqrt{2}}+3}$$$$$$ Answered by BaliramKumar last updated on 17/Nov/22 $$\sqrt{\frac{4}{\sqrt{2}}+3}$$$$\sqrt{\mathrm{2}\sqrt{\mathrm{2}\:}\:+\:\mathrm{3}\:} \…

Question Number 115033 by bobhans last updated on 23/Sep/20 $$Ifaandbpositiverealnumberwhere$$$$a^{505}+b^{505}=1,thenminimumvalue$$$$a^{2020}+b^{2020}is\mathrm{\_}\mathrm{\_}$$ Answered by 1549442205PVT last updated…