Since \[31z5\] is a multiple of 9, its sum of digits \[3+1+z+5=9+z\] is a multiple of 9; so \[9+z\] is one of these numbers: 0, 9, 18, 27, 36, 45, ... But since z is a digit, it can only be that \[9+z=9\] or 18. Therefore, \[z=0\] or 9.
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