How many primitive Pythagorean triples in arithmetic progression

Community Mathematics Centre, CoMaC (2012) How many primitive Pythagorean triples in arithmetic progression. At Right Angles, 1 (1). pp. 33-34.

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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 three-term AP with common difference 1. Naturally, our curiosity is alerted at this point.

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Articles in APF Magazines

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Community Mathematics Centre, CoMaC

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