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MathNet 2019-part-08 — 179 problems (EN–VI) Question 85

Math Olympiad Vault · MathNet 2019-part-08 — 179 problems (EN–VI)

Question 85

Let $a$, $b$, $c$ be positive integers such that
$$
\frac{a}{77} + \frac{b}{91} + \frac{c}{143} = 1
$$
What is the smallest possible value of $a + b + c$?