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2. Formulas for generating Pythagorean triples - Wikipedia

   en.wikipedia.org/wiki/Formulas_for_generating...

   To calculate a Pythagorean triple, take any term of this sequence and convert it to an improper fraction (for mixed number , the corresponding improper fraction is ). Then its numerator and denominator are the sides, b and a, of a right triangle, and the hypotenuse is b + 1. For example:

3. Help:Displaying a formula - Wikipedia

   en.wikipedia.org/wiki/Help:Displaying_a_formula

   MediaWiki stores rendered formulas in a cache so that the images of those formulas do not need to be created each time the page is opened by a user. To force the rerendering of all formulas of a page, you must open it with the getter variables action=purge&mathpurge=true .

4. Clearing denominators - Wikipedia

   en.wikipedia.org/wiki/Clearing_denominators

   The first step is to determine a common denominator D of these fractions – preferably the least common denominator, which is the least common multiple of the Q i. This means that each Q i is a factor of D, so D = R i Q i for some expression R i that is not a fraction. Then

5. Linear fractional transformation - Wikipedia

   en.wikipedia.org/wiki/Linear_fractional...

   In general, a linear fractional transformation is a homography of P(A), the projective line over a ring A.When A is a commutative ring, then a linear fractional transformation has the familiar form

6. Pythagorean triple - Wikipedia

   en.wikipedia.org/wiki/Pythagorean_triple

   Animation demonstrating the smallest Pythagorean triple, 3 2 + 4 2 = 5 2. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2. Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.

7. Boolean Pythagorean triples problem - Wikipedia

   en.wikipedia.org/wiki/Boolean_Pythagorean...

   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 + = are all the same color. For example, in the Pythagorean triple 3, 4, and 5 ( 3 2 + 4 2 = 5 2 {\displaystyle 3^{2}+4^{2}=5^{2}} ), if 3 and 4 are colored red, then 5 must be colored blue.