Question and Answers Forum

All Questions      Topic List

Number Theory Questions

Previous in All Question      Next in All Question      

Previous in Number Theory      Next in Number Theory      

Question Number 217244 by ArshadS last updated on 07/Mar/25

$$\mathrm{Find}\mathrm{all}\mathrm{two}-\mathrm{digit}\mathrm{numbers}\mathrm{such}\mathrm{that}$$$$\mathrm{when}\mathrm{the}\mathrm{number}\mathrm{is}\mathrm{divided}\mathrm{by}$$$$\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{its}\mathrm{digits}\mathrm{the}\mathrm{quotient}$$$$\mathrm{is}4\mathrm{and}\mathrm{the}\mathrm{remainder}\mathrm{is}3.$$

Answered by Frix last updated on 07/Mar/25

$$\frac{10a+b}{a+b}=4+\frac{3}{a+b}\wedge a+b>3$$$$\Rightarrow$$$$b=2a-1\wedge a+b>3$$$$a=2\wedge b=3$$$$a=3\wedge b=5$$$$a=4\wedge b=7$$$$a=5\wedge b=9$$$$S=\{23,35,47,59\}$$

Commented by ArshadS last updated on 10/Mar/25

$$\mathrm{Grateful}\mathrm{sir}!$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com