Category: Number Theory

Question Number 26410 by Joel578 last updated on 25/Dec/17 $$\mathrm{If}GCD(a,b)=1\mathrm{and}GCD(c,d)=1$$$$a\ne b\ne c\ne d\ne 1,a<b,c<d$$$$\mathrm{is}\mathrm{it}\mathrm{possible}\mathrm{that}\frac{a}{b}+\frac{c}{d}\mathrm{is}\mathrm{an}\mathrm{integer}\mathrm{number}?$$ Answered by mrW1 last updated on 25/Dec/17 $${since}\:{gcd}\left({c},{d}\right)=\mathrm{1},\:\frac{{c}}{{d}}\:{is}\:{already}\:{reduced} \…

Question Number 91448 by Cynosure last updated on 30/Apr/20 $$provethat1+x^{111}+x^{222}+x^{333}+x^{444}divides1+x^{111}+x^{222}+x^{333}+\dots \dots .+x^{999}$$ Commented by Cynosure last updated on…

Question Number 156419 by cortano last updated on 11/Oct/21 $$\mathrm{x}\mathrm{is}\mathrm{positive}\mathrm{integer}\mathrm{number}$$$$\mathrm{can}\mathrm{you}\mathrm{check}\mathrm{if}\mathrm{Q}=\sqrt[3]{({(\mathrm{x}+2)}^4-{\mathrm{x}}^4}$$$$\mathrm{is}\mathrm{a}\mathrm{natural}\mathrm{number}$$ Commented by mr W last updated on…

Question Number 25152 by tawa tawa last updated on 05/Dec/17 $$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{real}\mathrm{part}\mathrm{and}\mathrm{imaginary}\mathrm{part}\mathrm{of}\mathrm{the}\mathrm{complex}\mathrm{number}:\mathrm{z}={(1+\mathrm{i})}^{\mathrm{i}}$$ Commented by tawa tawa last updated on 05/Dec/17 $$\mathrm{please}\mathrm{help}.$$ Answered…

Question Number 156126 by VIDDD last updated on 08/Oct/21 $$\cos \frac{\pi }{5}=\dots ?\mathrm{with}\mathrm{solution}\mathrm{pls}$$ Commented by cortano last updated on 08/Oct/21 $$\frac{\pi }{5}=36°\Rightarrow \cos 72°=2\cos 36°-1$$$$\Rightarrow \cos 36°=\sqrt{\frac{1+\cos 72°}{2}}=\sqrt{\frac{1+\sin 18°}{2}}$$ Answered…