Category: Number Theory

Question Number 120049 by bramlexs22 last updated on 29/Oct/20 $$f(x+2)+f(x-2)=f\left(x\right)$$$$f\left(1\right)=1,f\left(2\right)=2,f\left(3\right)=3,f\left(4\right)=4$$$$thenf\left(100\right)=?$$ Answered by bemath last updated on 29/Oct/20 $$\Rightarrow{f}\left({x}−\mathrm{2}\right)−{f}\left({x}\right)+{f}\left({x}+\mathrm{2}\right)=\mathrm{0} \…

Question Number 119790 by bemath last updated on 27/Oct/20 $$Letx,y,zbenonnegativereal$$$$numbers,whichsatisfyx+y+z=1$$$$Findminimumvalueof$$$$Q=\sqrt{2-x}+\sqrt{2-y}+\sqrt{2-z}.$$ Answered by 1549442205PVT last updated on 27/Oct/20…

Question Number 119600 by bemath last updated on 25/Oct/20 $$Findgcdof{x}^4+x^3-4x^2+x+5$$$$and{x}^3+x^2-9x-9$$ Answered by TANMAY PANACEA last updated…

Question Number 53618 by kaivan.ahmadi last updated on 23/Jan/19 $$\mathrm{Let}\mathrm{x},\mathrm{y}\in \mathbb{Z}$$$$\mathrm{if}{\mathrm{x}}^2+{\mathrm{y}}^2\mathrm{divide}\mathrm{xy}+1\mathrm{then}\mathrm{prove}$$$$\frac{{\mathrm{x}}^2+{\mathrm{y}}^2}{\mathrm{xy}+1}\mathrm{is}\mathrm{square}\mathrm{of}\mathrm{integer}\mathrm{number}$$ Commented by mr W last…

Question Number 118880 by bemath last updated on 20/Oct/20 $$8(1+\frac{1}{2})(1+\frac{1}{2^2})(1+\frac{1}{2^4})(1+\frac{1}{2^8})\dots (1+\frac{1}{2^{32}})+\frac{1}{2^{60}}=?$$ Answered by Dwaipayan Shikari last updated on 20/Oct/20…