Category: Number Theory

Question Number 16880 by Tinkutara last updated on 27/Jun/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\mathrm{less}\:\mathrm{than}\:\mathrm{or}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{300}\:\mathrm{that}\:\mathrm{are} \\ $$$$\mathrm{multiples}\:\mathrm{of}\:\mathrm{3}\:\mathrm{or}\:\mathrm{5},\:\mathrm{but}\:\mathrm{are}\:\mathrm{not} \\ $$$$\mathrm{multiples}\:\mathrm{of}\:\mathrm{10}\:\mathrm{or}\:\mathrm{15}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 15889 by RasheedSoomro last updated on 15/Jun/17 $$\mathrm{Find}\:\mathrm{out}\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{non}}-\boldsymbol{\mathrm{five}}\:\boldsymbol{\mathrm{digit}}\:\mathrm{from}\:\mathrm{right} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}×\mathrm{3}×\mathrm{5}×…×\mathrm{625}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 15788 by tawa tawa last updated on 13/Jun/17 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{rational}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\:\mathrm{a}\:+\:\mathrm{b}\:=\:\mathrm{ab} \\ $$ Commented by mrW1 last updated on 14/Jun/17 $$\mathrm{b}=\frac{\mathrm{n}}{\mathrm{m}} \\ $$$$\mathrm{a}+\frac{\mathrm{n}}{\mathrm{m}}=\mathrm{a}×\frac{\mathrm{n}}{\mathrm{m}} \\ $$$$\left(\frac{\mathrm{n}}{\mathrm{m}}−\mathrm{1}\right)\mathrm{a}=\frac{\mathrm{n}}{\mathrm{m}}…

Question Number 15787 by tawa tawa last updated on 13/Jun/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{four}\:\mathrm{digits}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that}\:\:\mathrm{4}\:\centerdot\:\mathrm{abcd}\:=\:\mathrm{dcba} \\ $$ Commented by mrW1 last updated on 13/Jun/17 $$\mathrm{I}\:\mathrm{found}\:\mathrm{only}\:\mathrm{4}×\mathrm{2178}=\mathrm{8712} \\ $$ Commented by…

Question Number 15742 by RasheedSoomro last updated on 14/Jun/17 $$\mathrm{This}\:\mathrm{question}\:\mathrm{is}\:\mathrm{posted}\:\mathrm{on}\:\mathrm{the}\:\mathrm{request}\:\mathrm{of}\:\mathrm{mrW1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\left(\mathrm{See}\:\mathrm{comments}\:\mathrm{of}\:\mathrm{my}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{Q}#\mathrm{15543}\right). \\ $$$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{last}\:\:\boldsymbol{\mathrm{non}}-\boldsymbol{\mathrm{zero}}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\:\mathrm{2000}! \\ $$ Commented by mrW1 last updated…