科研之友
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摘要
In this note, we consider the Erdoos-Straus Diophantine equation c/n = 1/x + 1/v + 1/z, where n and c are positive integers with gcd(n, c) = 1. We provide a formula for the number f (n, c) of all positive integral solutions (x, y, z) of the equation. In 1948, Erd " os and Straus conjectured that f (n, 4) >= 1, for all integers n >= 2. Here, we solve the conjecture for a special case of n.
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单位常州工学院
