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MathNet 2019-part-01 — 184 problems (EN–VI) Question 166

Math Olympiad Vault · MathNet 2019-part-01 — 184 problems (EN–VI)

Question 166

Six-digit number $\overline{abcdef}$ is divisible by $3367$.
Prove that the sum $\overline{bcdefa} + \overline{fabcd}$ is divisible by $3367$ as well.
(As usual, by $\overline{xyz}$ we denote an integer number, which decimal representation consists of digits $x, y, \dots, z$ in that order)