MathDB

3

Part of 1993 Nordic

Problems(1)

system 3x3 with integers and numbers of their digits

Source: Nordic Mathematical Contest 1993 #3

10/5/2017
Find all solutions of the system of equations {s(x)+s(y)=xx+y+s(z)=zs(x)+s(y)+s(z)=y−4\begin{cases} s(x) + s(y) = x \\ x + y + s(z) = z \\ s(x) + s(y) + s(z) = y - 4 \end{cases} where x,yx, y, and zz are positive integers, and s(x),s(y)s(x), s(y), and s(z)s(z) are the numbers of digits in the decimal representations of x,yx, y, and zz, respectively.
system of equationsDigitspositive integernumber theory