But with a quick change of a couple of characters, I see that adding up two 4-digit numbers (having the same digits in different orders) never gives us 2003. But of course it can't, because all such would be even modulo 9 while 2003 is odd modulo 9.
Careful now, 7 * 2 = 14 == 5 (modulo 9).
In general (if I remember correctly), for any modulus q, if a does not share a factor with q there exists a b for every c such that a * b == c (modulo q).
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