منابع مشابه
Pythagorean Triples
Let n be a number. We say that n is square if and only if: (Def. 3) There exists m such that n = m2. Let us note that every number which is square is also natural. Let n be a natural number. Note that n2 is square. Let us observe that there exists a natural number which is even and square. Let us observe that there exists a natural number which is odd and square. Let us mention that there exist...
متن کاملPythagorean Triples
The name comes from elementary geometry: if a right triangle has leg lengths x and y and hypotenuse length z, then x + y = z. Of course here x, y, z are positive real numbers. For most integer values of x and y, the integer x + y will not be a perfect square, so the positive real number √ x2 + y2 will be irrational: e.g. x = y = 1 =⇒ z = √ 2. However, a few integer solutions to x + y = z are fa...
متن کاملAre monochromatic Pythagorean triples avoidable?
A Pythagorean triple is a triple of positive integers a,b,c ∈ N+ satisfying a2 + b2 = c2. Is it true that, for any finite coloring of N+, at least one Pythagorean triple must be monochromatic? In other words, is the Diophantine equation X2 +Y 2 = Z2 regular? This problem has been open since several decades, even restricted to 2-colorings. In this note, we introduce partial morphisms, which are ...
متن کاملPythagorean Triples and Cryptographic Coding
This paper summarizes basic properties of PPTs and shows that each PPT belongs to one of six different classes. Mapping an ordered sequence of PPTs into a corresponding sequence of these six classes makes it possible to use them in cryptography. We pose problems whose solution would facilitate such cryptographic application. Introduction A Pythagorean triple (a, b, c) consists of positive integ...
متن کاملThe dynamics of Pythagorean triples
We construct a piecewise onto 3-to-1 dynamical system on the positive quadrant of the unit circle, such that for rational points (which correspond to normalized Primitive Pythagorean Triples), the associated ternary expansion is finite, and is equal to the address of the PPT on Barning’s [9] ternary tree of PPTs, while irrational points have infinite expansions. The dynamical system is conjugat...
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ژورنال
عنوان ژورنال: Journal of Mathematics Research
سال: 2021
ISSN: 1916-9809,1916-9795
DOI: 10.5539/jmr.v13n3p63