ERDÖS – STRAUSS SANISI ÜZERİNE
ERDÖS – ON STRAUSS SECURITY

Summary/Abstract: In this study, known as Erdös-Strauss Conjugation, a ≥ 2 integers, x, y, z being positive integers; Integer solutions (x, y, z) that satisfy the equation 1/𝑥 + 1/𝑦 + 1/𝑧 = 4/𝑎 have been studied. My goal is to find the solution sets of this equation, if any. In this study, the result of the equation 1/𝑥 + 1/𝑦 = 1/𝑎 , where x, y is a natural number greater than one, is examined as a unit fraction. Then, the result of the equation 1/𝑥 + 1/𝑦 = 𝑏/𝑎 is examined when it is a positive simple fraction. Finally, the solution sets of the equation 1/𝑥 + 1/𝑦 + 1/𝑧 = 4/𝑎 were examined. As a result of the studies, when the number a is the prime number greater than 5 and the number a is the only non-prime number, there is no solution set when all prime factors are one and the remainder of the division by 3 is one. Apart from that, there is a solution set for all positive integers a.

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