Question

what is BOOLEAN PYTHAGOREA N TRIPLES PROBLEM? PLEASE TELL ME ANY​

Answer 1

Answer:

The Boolean Pythagorean triples problem.

• Statement:- The problem asks if it is possible to color each of the positive integers either red or blue, so that no Pythagorean triple of integers a, b, c, satisfying {\displaystyle a^{2}+b^{2}=c^{2}}a^{2}+b^{2}=c^{2} are all the same color.
• For example, in the Pythagorean triple 3, 4 and 5 ({\displaystyle 3^{2}+4^{2}=5^{2}}3^{2}+4^{2}=5^{2}), if 3 and 4 are colored red, then 5 must be colored blue.

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Answer 2

Boolean Pythagorean triples problem

The boolean Pythagorean Triples problem has been a long- standing open problem in Ramsey Theory: Can the set N = {1, 2,... } of natural numbers be divided into two parts, such that no part contains a triple (a, b, c) with a2 + b2 = c2 ? A prize for the solution was offered by Ronald Graham over two decades ago.

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