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KURSCHAK 1980 Problem 2

    Let n>1n > 1 be an odd integer. Prove that a necessary and sufficient condition for the existence of positive integers xx and yy satisfying 4n=1x+1y\frac{4}{n}=\frac{1}{x}+\frac{1}{y} is that nn has a prime divisor of the form 4k−14k - 1 .

    Dataset text AI-MO AoPS. Quoted with source.

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