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MathNet 2019-part-07 — 184 problems (EN–VI) Question 81

Math Olympiad Vault · MathNet 2019-part-07 — 184 problems (EN–VI)

Question 81

Are there integers $a \lt b \lt c \lt d$ such that
$$
\frac{a}{a} + \frac{a}{b} + \frac{a}{c} + \frac{a}{d} = \frac{b}{a} + \frac{b}{b} + \frac{b}{c} + \frac{b}{d} ?
$$