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1111 divides four-digit number plus product of digits

Source: Canada Repêchage 2014/3

June 18, 2016
number theoryDivisibility

Problem Statement

Let 1000≤n=ABCD10≤99991000 \leq n = \text{ABCD}_{10} \leq 9999 be a positive integer whose digits ABCD\text{ABCD} satisfy the divisibility condition: 1111∣(ABCD+AB×CD).1111 | (\text{ABCD} + \text{AB} \times \text{CD}). Determine the smallest possible value of nn.
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