Question Number 55701 by mathaddicted last updated on 02/Mar/19 $${Is}\:{true}\:{or}\:{not}\:{that}\:\mathrm{4181}\:{is}\:{the}\:{only}\:{one} \\ $$$${Fibonacci}'{s}\:{number}\:{with}\:{no}\:{prime}\:{factor} \\ $$$${which}\:{is}\:{also}\:{a}\:{Fibonacci}'{s}\:{number}? \\ $$ Commented by MJS last updated on 03/Mar/19 $$\mathrm{1346269}=\mathrm{557}×\mathrm{2417} \\…
Question Number 55631 by Tawa1 last updated on 28/Feb/19 Answered by tanmay.chaudhury50@gmail.com last updated on 01/Mar/19 $$\left(\mathrm{1}−{x}\right)^{\frac{−\mathrm{1}}{\mathrm{2}}} \\ $$$$=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{x}+\frac{\mathrm{1}×\mathrm{3}}{\mathrm{2}×\mathrm{4}}{x}^{\mathrm{2}} +\frac{\mathrm{1}×\mathrm{3}×\mathrm{5}}{\mathrm{2}×\mathrm{4}×\mathrm{6}}{x}^{\mathrm{3}} +… \\ $$$$\boldsymbol{{L}}{HS} \\ $$$$\mathrm{1}+\frac{\mathrm{4}}{\mathrm{10}}+\frac{\mathrm{4}×\mathrm{12}}{\mathrm{10}×\mathrm{20}}+\frac{\mathrm{4}×\mathrm{12}×\mathrm{20}}{\mathrm{10}×\mathrm{20}×\mathrm{30}}+……
Question Number 55476 by pooja24 last updated on 25/Feb/19 $$\mathrm{4}\:{metal}\:{rods}\:{of}\:{length}\:\mathrm{78}\:{cm},\mathrm{104}\:{cm},\mathrm{117}{cm}, \\ $$$${a}.{nd}\:\mathrm{169}\:{cm}\:{are}\:{to}\:{be}\:{cut}\:{into}\:{parts}\:{of}\:{equal}\:{length} \\ $$$${Each}\:{length}\:{must}\:{be}\:{as}\:{long}\:{as}\:{possible} \\ $$$${What}\:{is}\:{the}\:{maximum}\:{number}\:{of}\:{pieces} \\ $$$${that}\:{can}\:{be}\:{cut}? \\ $$ Answered by Joel578 last updated…
Question Number 120923 by bemath last updated on 04/Nov/20 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{primes}\:{p}\:\mathrm{for}\:\mathrm{which} \\ $$$$\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}\: \\ $$$$\begin{cases}{{p}\:+\mathrm{1}\:=\:\mathrm{2x}^{\mathrm{2}} }\\{{p}^{\mathrm{2}} +\mathrm{1}=\mathrm{2y}^{\mathrm{2}} \:\:}\end{cases}\:;\:\mathrm{has}\:\mathrm{solution}\:\mathrm{in} \\ $$$$\mathrm{integers}\:\mathrm{x},\:\mathrm{y}. \\ $$ Answered by liberty last…
Question Number 120812 by bramlexs22 last updated on 03/Nov/20 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{integral}\:\mathrm{solutions}\:\mathrm{to}\: \\ $$$$\mathrm{the}\:\mathrm{equation}\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{y}^{\mathrm{2}} +\mathrm{1}\right)+\mathrm{2}\left(\mathrm{x}−\mathrm{y}\right)\left(\mathrm{1}−\mathrm{xy}\right)=\mathrm{4}\left(\mathrm{1}+\mathrm{xy}\right) \\ $$ Answered by liberty last updated on 03/Nov/20 $$\Leftrightarrow\:\left(\mathrm{xy}−\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{x}−\mathrm{y}\right)^{\mathrm{2}}…
Question Number 120679 by kaivan.ahmadi last updated on 02/Nov/20 $${h} \\ $$ Commented by bobhans last updated on 01/Nov/20 $$\sqrt[{\mathrm{3}}]{−\mathrm{8}}\: \\ $$$$\left(\mathrm{1}.\mathrm{0}\:+\:\mathrm{1}.\mathrm{732051i}\right) \\ $$ Commented…
Question Number 120563 by rexfordattacudjoe last updated on 01/Nov/20 $${A}\:{man}\:{has}\:{a}\:{wife}\:{with}\:{six} \\ $$$${children}\:{and}\:{his}\:{total}\:{income}\:{is} \\ $$$${Gh\$}\mathrm{8500}.{He}\:{was}\:{allowed}\:{the} \\ $$$${following}\:{free}\:{tax} \\ $$$${personal}:……\$\mathrm{1200} \\ $$$${wife}:………..\$\mathrm{300} \\ $$$${each}\:{child}:…..\$\mathrm{250}\:{for}\:{a}\:{maximum}\:{of}\:\mathrm{4} \\ $$$${dependant}\:{relative}:\$\mathrm{400} \\…
Question Number 54897 by gunawan last updated on 14/Feb/19 $$\mathrm{Find}\:\mathrm{value}\:\mathrm{of}\:{n}\:\mathrm{so}\:\mathrm{120}\:\mid\:\mathrm{5}{n}\left({n}^{\mathrm{2}} −\mathrm{1}\right) \\ $$ Commented by jahanara@gmail.com last updated on 02/May/19 $${so}\:{easy} \\ $$ Answered by…
Question Number 120202 by bemath last updated on 30/Oct/20 $${Show}\:{for}\:{the}\:{equation}\:{a}^{{n}} \:=\:{b}^{\mathrm{2}} −\mathrm{1}\: \\ $$$${where}\:{n}>\mathrm{1}\:{and}\:{a}>\mathrm{2}\:{are}\:{any}\:{natural} \\ $$$${numbers}\:,\:{there}\:{are}\:{no}\:{positive}\:{integer} \\ $$$${solutions}\:{for}\:{a}\:{and}\:{b}\:? \\ $$ Terms of Service Privacy Policy…
Question Number 120049 by bramlexs22 last updated on 29/Oct/20 $$\:{f}\left({x}+\mathrm{2}\right)+{f}\left({x}−\mathrm{2}\right)={f}\left({x}\right) \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{1}\:,{f}\left(\mathrm{2}\right)=\mathrm{2},{f}\left(\mathrm{3}\right)=\mathrm{3},{f}\left(\mathrm{4}\right)=\mathrm{4} \\ $$$${then}\:{f}\left(\mathrm{100}\right)=? \\ $$ 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} \\…