A STUDY ON PYTHAGOREAN TRIPLES

The Pythagorean numbers play a significant role in the theory of higher arithmetic as they come in the majority of indeterminate problem. For the discovery of the law of the three squares (Pythagorean equation), really, one should be indebted to the Pythagorean who were the first Greeks with great intellectual perception. One may notice to his surprise that the Egyptians, the Chinese, the Babylonians and the Indians knew some knowledge of the property of right angled Pythagorean triangles or Pythagorean numbers .Since there is a 1−1 correspondence between Pythagorean numbers and Pythagorean triangles, we shall use them interchangeably. The only geometrical theorem with which the ancient Chinese were acquainted is that the area of the square described on the hypotenuse of a right angled triangle is equal to the sum of the areas of the squares described on the sides. A Pythagorean triangle is a right triangle whose sides are integral lengths