Integer triangle formula_112 and formula_113 generate the same triple. Unfortunately the two pairs can both be of gcd=3, so we can't avoid duplicates by simply skipping that case. Instead, duplicates can be avoided by formula_27 going only till formula_115. Note that we still need to divide by 3 if gcd=3. The only solution for formula_116 under the above constraints is formula_117 for formula_118. With this additional formula_119 constraint all triples can be generated uniquely. An Eisenstein triple is a set of integers which are the lengths of the sides of a triangle where one of the angles is 60 degrees. Integer triangles
What Is the Third Estate? What Is the Third Estate? What Is the Third Estate? () is a political pamphlet written in January 1789, shortly before the outbreak of the French Revolution, by the French thinker and clergyman Abbé Emmanuel Joseph Sieyès (1748–1836). The pamphlet was Sieyès' response to finance minister Jacques Necker's invitation for writers to state how they thought the Estates-General should be organized. In the pamphlet, Sieyès argues that the third estate – the common people of France – constituted a complete nation within itself and had no need of the "dead weight" of the two other orders, the first and second