Question Number 113003 by Aina Samuel Temidayo last updated on 10/Sep/20 $$\mathrm{The}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{a}\:\mathrm{three}−\mathrm{digit}\:\mathrm{number}\:\mathrm{A} \\ $$$$\mathrm{are}\:\mathrm{written}\:\mathrm{in}\:\mathrm{the}\:\mathrm{reverse}\:\mathrm{order}\:\mathrm{to} \\ $$$$\mathrm{form}\:\mathrm{another}\:\mathrm{three}−\mathrm{digit}\:\mathrm{number}\:\mathrm{B}. \\ $$$$\mathrm{If}\:\mathrm{B}>\mathrm{A}\:\mathrm{and}\:\mathrm{B}−\mathrm{A}\:\mathrm{is}\:\mathrm{perfectly} \\ $$$$\mathrm{divisible}\:\mathrm{by}\:\mathrm{7}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of} \\ $$$$\mathrm{values}\:\mathrm{of}\:\mathrm{A}. \\ $$ Commented…
Question Number 113001 by Aina Samuel Temidayo last updated on 10/Sep/20 $$\mathrm{N}!\:\mathrm{is}\:\mathrm{completely}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{13}^{\mathrm{52}} . \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{smallest}\:\mathrm{such}\:\mathrm{number}\:\mathrm{N}? \\ $$ Commented by MJS_new last updated on…
Question Number 112999 by Aina Samuel Temidayo last updated on 10/Sep/20 $$\mathrm{Product}\:\mathrm{of}\:\mathrm{divisors}\:\mathrm{of}\:\mathrm{7056}\:? \\ $$ Answered by mr W last updated on 10/Sep/20 $$\mathrm{7056}=\mathrm{2}^{\mathrm{4}} ×\mathrm{3}^{\mathrm{2}} ×\mathrm{7}^{\mathrm{2}}…
Question Number 112998 by Aina Samuel Temidayo last updated on 10/Sep/20 $$\mathrm{If}\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{1}\:\mathrm{and}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\mathrm{are}\:\mathrm{positive} \\ $$$$\mathrm{real}\:\mathrm{numbers},\:\mathrm{then}\:\mathrm{the}\:\mathrm{least}\:\mathrm{value}\:\mathrm{of} \\ $$$$\left(\frac{\mathrm{1}}{\mathrm{x}}−\mathrm{1}\right)\left(\frac{\mathrm{1}}{\mathrm{y}}−\mathrm{1}\right)\left(\frac{\mathrm{1}}{\mathrm{z}}−\mathrm{1}\right)\:\mathrm{is}\: \\ $$ Answered by MJS_new last updated on 11/Sep/20…
Question Number 112996 by Aina Samuel Temidayo last updated on 10/Sep/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{19}^{\mathrm{81}} +\mathrm{4}^{\mathrm{9k}} ,\:\mathrm{k}\in\mathrm{N} \\ $$ Answered by Aziztisffola last updated on 10/Sep/20…
Question Number 112994 by Aina Samuel Temidayo last updated on 10/Sep/20 $$\mathrm{If}\:\mathrm{n}\:\mathrm{is}\:\mathrm{any}\:\mathrm{even}\:\mathrm{number},\:\mathrm{then} \\ $$$$\mathrm{n}\left(\mathrm{n}^{\mathrm{2}} +\mathrm{20}\right)\:\mathrm{is}\:\mathrm{always}\:\mathrm{divisible}\:\mathrm{by}? \\ $$ Answered by mr W last updated on 10/Sep/20…
Question Number 47310 by Meritguide1234 last updated on 08/Nov/18 Commented by MJS last updated on 08/Nov/18 $${x}\neq{y}\neq{z}\neq\mathrm{0}\:\mathrm{I}\:\mathrm{guess}. \\ $$$$\mathrm{but}\:\mathrm{we}\:\mathrm{know}\:\mathrm{that}\:\mathrm{there}'\mathrm{s}\:\mathrm{no}\:\mathrm{triple}\:{xyz}\:\mathrm{for}\:{n}>\mathrm{2} \\ $$$$\mathrm{so}\:\mathrm{we}\:\mathrm{only}\:\mathrm{have}\:\mathrm{to}\:\mathrm{show}\:\mathrm{for}\:{n}=\mathrm{2}\:\mathrm{and}\:\mathrm{in}\:\mathrm{this} \\ $$$$\mathrm{case}\:\mathrm{it}'\mathrm{s}\:\mathrm{obviously}\:\mathrm{true}\: \\ $$…
Question Number 178277 by Sheshdevsahu last updated on 14/Oct/22 $$ \\ $$$${if}\:\mathrm{2}^{{pq}} −\mathrm{2}^{{rs}} =\mathrm{32};\:{where}\:{p},{q},{r},{s}\in\mathbb{Z}\: \\ $$$${then}\:{possible}\:{values}\:{of} \\ $$$${p}\:+\:{q}\:+\:{r}\:+\:{s}\:=\:?? \\ $$$$ \\ $$ Terms of Service…
Question Number 178282 by Sheshdevsahu last updated on 14/Oct/22 $$ \\ $$$${find}\:{unit}\:{digit}\:{of}\: \\ $$$$\mathrm{1}^{\mathrm{1}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{3}} +…….+\mathrm{63}^{\mathrm{63}} +\mathrm{64}^{\mathrm{64}} \\ $$ Answered by mr W last…
Question Number 112575 by Aina Samuel Temidayo last updated on 08/Sep/20 Answered by Rasheed.Sindhi last updated on 09/Sep/20 $${x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} =\mathrm{1376} \\ $$$$\because\mathrm{4}\mid\mathrm{1376}\:\:\:\:\:\therefore\:\mathrm{4}\mid{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} \\…