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To find a solution for , just divide all of the unit fractions in the solution for by : = + + = + +. If 4 n {\displaystyle {\tfrac {4}{n}}} were a counterexample to the conjecture, for a composite number n {\displaystyle n} , every prime factor p {\displaystyle p} of n {\displaystyle n} would also provide a counterexample 4 p {\displaystyle ...
The Erdős–Gyárfás conjecture on cycles with lengths equal to a power of two in graphs with minimum degree 3.; The Erdős–Hajnal conjecture that in a family of graphs defined by an excluded induced subgraph, every graph has either a large clique or a large independent set.
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Scammers are using AI-powered voice-cloning tools to prey on people. But experts say there's a simple way to protect you and your family.
Before you add the eggs to the cold skillet, add a bit of butter and, if you have it, crème fraîche. The butter will melt slowly with the eggs, adding flavor and richness. The crème fraîche ...
The idea of the Erdős number was originally created by the mathematician's friends as a tribute to his enormous output. Later it gained prominence as a tool to study how mathematicians cooperate to find answers to unsolved problems. Several projects are devoted to studying connectivity among researchers, using the Erdős number as a proxy. [7]
One can interpret the positions of the numbers in a sequence as x-coordinates of points in the Euclidean plane, and the numbers themselves as y-coordinates; conversely, for any point set in the plane, the y-coordinates of the points, ordered by their x-coordinates, forms a sequence of numbers (unless two of the points have equal x-coordinates).