Spain Mathematical Olympiad Problem 3

Find the largest integer NN satisfying the following two conditions:

(i) N3\lfloor \frac N3 \rfloor consists of three equal digits;

(ii) N3=1+2+3++n\lfloor \frac N3 \rfloor = 1 + 2 + 3 +\cdots + n for some positive integer n.n.

\lfloor \cdot \rfloor denotes the floor function.

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