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MathNet 2021 — Part 09 Question 27

Math Olympiad Vault · MathNet 2021 — Part 09

Question 27

Is it possible for positive integers $a,d$ to satisfy each of the following equalities?

- **(a)** $[a,a+d]=[a,a+2d]$.

- **(b)** $[a,a+d]=[a,a+4d]$.

Here $[x,y]$ denotes the least common multiple of the integers $x,y$.