Very nice going CPhill!!!. But, with little help from a simple computer code, we can do a bit better!.
A*1,103 + 1,041 =B*1,303 + 859 = C*2,003 + 1,095, solve for A, B, C.
A = 40, B = 34, C = 22. Therefore, the smallest positive number will be: 40 x 1,103 + 1,041 =45,161.
The general formula will then be:
LCM{1,103, 1,303, 2003} = 2,878,729,627
2,878,729,627D + 45,161 = n. For D =0, 1, 2.....etc. we have:
45,161, 2,878,774,788, 5,757,504,415.....etc.