Question Number 475 by 123456 last updated on 25/Jan/15 $${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$${if}\:{p}\:{is}\:{prime}\:{and}\:{n}\in\mathbb{N},\mathrm{1}<{n}\leqslant{p} \\ $$$${then}\:{pn}−\mathrm{1}\:{is}\:{prime} \\ $$ Answered by prakash jain last updated on 11/Jan/15 $${p}=\mathrm{5}…
Question Number 131547 by liberty last updated on 06/Feb/21 $$\:\mathrm{J}\:=\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{x}^{\mathrm{8}} −\mathrm{1}}{\mathrm{x}^{\mathrm{10}} +\mathrm{1}}\:\mathrm{dx}\:? \\ $$ Answered by rs4089 last updated on 06/Feb/21 $$\mathrm{0} \\…
Question Number 131546 by mathmax by abdo last updated on 05/Feb/21 $$\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{x}} \mathrm{ln}\left(\mathrm{x}\right)\mathrm{dx}\:=−\gamma \\ $$ Answered by Dwaipayan Shikari last updated on 06/Feb/21…
Question Number 472 by 123456 last updated on 25/Jan/15 $${proof}\:{or}\:{give}\:{a}\:{counter}−{example}: \\ $$$${if}\:{nm}\:{is}\:{prime}\:{then}\:\mathrm{mdc}\left({n}^{\mathrm{2}} ,{m}^{\mathrm{2}} \right)=\mathrm{1} \\ $$ Answered by prakash jain last updated on 10/Jan/15 $$\mathrm{If}\:{n},{m}\:\in\mathbb{Z}\:\mathrm{then}\:{n}=\mathrm{1}\:\mathrm{or}\:{m}=\mathrm{1}…
Question Number 131541 by 0731619177 last updated on 05/Feb/21 Answered by asdaldeen last updated on 05/Feb/21 $$\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 471 by 123456 last updated on 25/Jan/15 $${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$${if}\:{n}^{\mathrm{2}} \:{is}\:{prime},\:{then}\:{n}\notin\mathbb{Z} \\ $$ Answered by prakash jain last updated on 10/Jan/15 $${n}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{prime}\:\mathrm{so}\:{n}^{\mathrm{2}}…
Question Number 66004 by salahahmed last updated on 07/Aug/19 $${x}^{{x}^{{x}^{\iddots} } } =\mathrm{3} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x} \\ $$ Answered by mr W last updated on 07/Aug/19…
Question Number 469 by 123456 last updated on 25/Jan/15 $${proof}\:{or}\:{given}\:{a}\:{counter}−{example} \\ $$$${if}\:{p}\:{is}\:{prime}\:{and}\:{a}\in\mathbb{N}\:{then} \\ $$$${p}\mid\left({a}+{p}\right)^{{p}} −{a}^{{p}} \\ $$ Answered by prakash jain last updated on 10/Jan/15…
Question Number 66005 by mathmax by abdo last updated on 07/Aug/19 $${solve}\:\:\:{x}^{\mathrm{2}} {y}^{''} \:+{xy}^{'} −\mathrm{3}{y}\:=\mathrm{4}{e}^{−{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 465 by shubham last updated on 09/Jan/15 $${A}\:{particle}\:{moves}\:{with}\:{a}\:{central}\:{acceration}\:{varies}\:{as}\:{the}\:{cube}\:{of}\:{the}\:{distance}.\:{if}\:{it}\:{be}\:{projected}\:{from}\:{an}\:{apse}\:{at}\:{distance}\:{a}\:{from}\:{the}\:{origin}\:{with}\:{a}\:{velocity}\:{which}\:{is}\:\sqrt{\mathrm{2}\:}\:{times}\:{the}\:{velocity}\:{for}\:{a}\:{circle}\:{of}\:{radius}\:{a}.\:{show}\:{that}\:{the}\:{equation}\:{of}\:{path}\:{is}\:{its}\:{r}\mathrm{cos}\theta/\sqrt{\mathrm{2}}\:=\:{a} \\ $$ Commented by prakash jain last updated on 09/Jan/15 $$\mathrm{Reformatted} \\ $$$${A}\:{particle}\:{moves}\:{with}\:{a}\:{central} \\ $$$${acceration}\:{varies}\:{as}\:{the}\:{cube}\:…