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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Erd s Straus conjecture states that for all integers n 2, the rational number 4/n can be expressed as the sum of three unit fractionsThe Hasse principle for Diophantine equations asserts that, to solve such an equation over the integers, we should combine solutions obtained modulo each possible prime number. On the face of it this principle makes little sense for the Erd s Straus conjecture, as the equation 4xyz=n(xy+xz+yz) is easily solvable modulo any prime. Nevertheless, modular identities have proven a very important tool in the study of the conjecture.