Question Number 119657 by bemath last updated on 26/Oct/20 $${Suppose}\:{that}\:{the}\:{greatest}\:{common}\:{divisor}\:{of} \\ $$$${the}\:{positive}\:{integers}\:{a},{b}\:{and}\:{c}\:{is}\:\mathrm{1}\:{and} \\ $$$$\frac{{ab}}{{a}−{b}}\:=\:{c}\:.\:{Prove}\:{that}\:{a}−{b}\:{is}\:{a} \\ $$$${perfect}\:{square} \\ $$ Commented by som(math1967) last updated on 26/Oct/20…
Question Number 119600 by bemath last updated on 25/Oct/20 $${Find}\:{gcd}\:{of}\:{x}^{\mathrm{4}} +{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} +{x}+\mathrm{5}\: \\ $$$${and}\:{x}^{\mathrm{3}} +{x}^{\mathrm{2}} −\mathrm{9}{x}−\mathrm{9} \\ $$ Answered by TANMAY PANACEA last updated…
Question Number 53620 by kaivan.ahmadi last updated on 23/Jan/19 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{2n}+\mathrm{1}}\:=? \\ $$$$ \\ $$$$\mathrm{1}.\:\frac{\pi}{\mathrm{4}}\:\:\:\:\:\:\:\:\mathrm{2}.\:\frac{\pi^{\mathrm{2}} }{\mathrm{12}}\:\:\:\:\:\mathrm{3}.\:\frac{\pi}{\mathrm{8}}\:\:\:\:\:\mathrm{4}.\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$ Commented by turbo msup…
Question Number 53618 by kaivan.ahmadi last updated on 23/Jan/19 $$\mathrm{Let}\:\mathrm{x},\mathrm{y}\in\mathbb{Z} \\ $$$$\mathrm{if}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:\mathrm{divide}\:\mathrm{xy}+\mathrm{1}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }{\mathrm{xy}+\mathrm{1}}\:\mathrm{is}\:\mathrm{square}\:\mathrm{of}\:\mathrm{integer}\:\mathrm{number} \\ $$ Commented by mr W last…
Question Number 119094 by syamil last updated on 22/Oct/20 $${Why}\:{the}\:{Fermat}\:{formula}\:{about}\:{prime}\:{numbers}\:{is}\:{for}\:{n}\:=\:\mathrm{5}\:{and}\:{n}\:=\:\mathrm{6}\:{fail}? \\ $$$$ \\ $$$${f}\left({n}\right)\:=\:\mathrm{2}^{\mathrm{2}^{{n}} } \:+\:\mathrm{1} \\ $$ Answered by 1549442205PVT last updated on 22/Oct/20…
Question Number 118880 by bemath last updated on 20/Oct/20 $$\mathrm{8}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{4}} }\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{8}} }\right)…\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{32}} }\right)+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{60}} }=? \\ $$ Answered by Dwaipayan Shikari last updated on 20/Oct/20…
Question Number 53048 by D-Quant last updated on 16/Jan/19 Commented by tanmay.chaudhury50@gmail.com last updated on 17/Jan/19 $${excellent}\:{question}…{pls}\:{wait}… \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 183998 by JDamian last updated on 01/Jan/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{natural}\:\mathrm{number}\:\boldsymbol{\mathrm{n}}\:{such} \\ $$$$\:\:\:\:\:\:\:{n}=\mathrm{7}^{{a}} \centerdot\mathrm{17}^{{b}} \:\:\:\:\:\:{a}\in\mathbb{N},\:\:\:{b}\in\mathbb{N} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{its}\:\mathrm{divisors}\:\left(\mathrm{1}\:\mathrm{and}\right. \\ $$$$\left.\boldsymbol{\mathrm{n}}\:\mathrm{included}\right)\:\mathrm{is}\:\mathrm{2456}. \\ $$ Commented by Rasheed.Sindhi last updated…
Question Number 118362 by Ar Brandon last updated on 17/Oct/20 $$\mathrm{Prove}\:\mathrm{that}\:\boldsymbol{\pi}\:\mathrm{is}\:\mathrm{an}\:\mathrm{irrational}\:\mathrm{number} \\ $$ Answered by MJS_new last updated on 17/Oct/20 $$\mathrm{search}\:\mathrm{the}\:\mathrm{www} \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{several}\:\mathrm{proofs},\:\mathrm{no}\:“\mathrm{easy}''\:\mathrm{one}. \\ $$…
Question Number 118357 by conclaude last updated on 17/Oct/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{prime}\:\mathrm{factors}\:\mathrm{of} \\ $$$$\mathrm{20}^{\mathrm{5}} +\mathrm{21}. \\ $$ Answered by MJS_new last updated on 17/Oct/20 $$\mathrm{20}^{\mathrm{5}} +\mathrm{21}=\mathrm{3200021}=\mathrm{11}×\mathrm{421}×\mathrm{691} \\…