A familiar example is a

Pythagorean triple (a2+b2=c2).

For this we would use the

Pythagorean triples. We propose an elegant solution by adding two

Pythagorean triples to obtain a new

Pythagorean triple.

Consequently, those dates received some points, but not as many as dates in which the three numbers form a

Pythagorean triple, which only happens 50 times a century.

A

Pythagorean triple is a set of three integers which occur as the side lengths of a right-angled triangle.

Keywords The Smarandache function,

Pythagorean triple, equation, positive integer solutions.

As for a

Pythagorean triple (x, y, z) satisfying the relation [x.sup.2] + [y.sup.2] = [z.sup.2], all the triples ([??]x, [??]y, [??]z) will also be solutions, implying [N.sub.p] = 8.(p - 1/2.p - 5/4) = (p-1).(p-5) and [N.sub.p] = 8.(p - 1/2.p - 3/4) = (p - 1).(p - 3), respectively.

Did you know, too, that if you take any

Pythagorean triple, such as 3, 4, 5 or 5, 12, 13, and multiply the three numbers, the result is always a multiple of 60?

They have variously interpreted the cryptic columns of numbers, written in the wedge-shaped script called cuneiform, as a trigonometric table or a sophisticated scheme for generating

Pythagorean triples. A

Pythagorean triple is a set of three whole numbers, a, b, and c, such that a[super]2 + b[super]2 = C[super]2.

The relationship, [a.sup.2] + [b.sup.2] = [c.sup.2] for whole numbers like (3,4,5), is called a

Pythagorean Triple. Even with the formula, it has been very difficult to calculate exact triples.

Trial and error with the

Pythagorean triple {3,4,5} soon establishes that x = 32 and y = 24.

These two numbers form two parts of a

Pythagorean Triple: [39.sup.2] + [80.sup.2] = [89.sup.2].

However, when a, b, c are all integers and obey equation (1), they are referred to as a

Pythagorean triple [a, b, c].