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$$n = 1111\ldots11$$ is a 2026-digit number with each digit as 1. If $$n$$ is divided by 1111, then the quotient is $$Q$$ and the remainder is $$R$$, then
Since $$2026 = 2 + 4 \times 506$$, write $$n = 11 \times 10^{2024} + \underbrace{11\ldots1}_{2024}$$, and the repunit with 2024 ones is a multiple of 1111. As $$10^4 = 9999 + 1$$ leaves remainder 1 on division by 1111, $$10^{2024}$$ also leaves remainder 1, so $$R = 11$$. Dividing a 2026-digit number beginning with 11 by the 4-digit number 1111 gives a quotient of $$2026 - 3 = 2023$$ digits.
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