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system 3x3 with integers and numbers of their digits

Source: Nordic Mathematical Contest 1993 #3

October 5, 2017
system of equationsDigitspositive integernumber theory

Problem Statement

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.
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