Overtly Covert

Number Theory Level pending

abcdef is a 6 digit number which on dividing by 6 gives defabc as the quotient. Find the number.

1 solution

James Moors
Apr 23, 2015

Let $x=\overline{abc}, y = \overline{def}$ . Now this reduces to:

$\begin{aligned} 1000x + y &= 6(x+1000y) \\ \Rightarrow 994x &= 5999y\\ \Rightarrow 142x &= 857y \end{aligned}$

Since $142$ and $857$ are coprime, the only valid solution is $x=857, y=142$ .