Community Mathematics Centre, CoMaC
(2012)
How many primitive Pythagorean triples in arithmetic progression.
At Right Angles, 1 (1).
pp. 3334.
Abstract
Everyone knows that (3, 4, 5) is a Pythagorean triple (‘PT’);
for, the numbers satisfy the Pythagorean relation 3^2 +4^2 =5^2. Indeed, it is a Primitive Pythagorean triple (‘PPT’) since the integers in the triple are coprime. (See the Problem Corner for definitions of unfamiliar terms.) But this triple has a further property: its entries are in arithmetic progression for, 3, 4, 5 forms a threeterm AP with common difference 1. Naturally, our curiosity is alerted at this point.
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