If a Pythagorean triple is a multiple of $(3, 4, 5)$ and one member is $20$, the smallest member is

If a Pythagorean triple is a multiple of $(3, 4, 5)$ and one member is $20$, the smallest member is
  1. $15$
  2. $12$
  3. $20$
  4. $25$

Solution

$20 = 4 \times 5$, so the scale is $5$, giving $(15, 20, 25)$. Smallest $= 15$.

Asked in: IMO

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