CEMC Pascal

Algebra Difficulty 2.1 Junior Find the answer

How many triples $(a, b, c)$ of positive integers satisfy the conditions $6ab = c^2$ and $a < b < c \leq 35$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

There are 8 such triplets: $(2,3,6), (3,8,12), (4,6,12), (6,9,18), (6,16,24), (8,12,24), (6,25,30), (10,15,30)$ .

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