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The Erdős-Straus conjecture, due to Paul Erdős and E. G. Straus, states that for every integer 
, the Diophantine
equation
 |
has a solution in positive integers 
, 
,
and 
(Obláth 1950, Rosati 1954, Bernstein 1962, Yamamoto 1965, Vaughan 1970, Guy
1994). Swett (1999) verified the conjecture for 
. Salez (2014) extended the computation
to 
, and Mihnea and Dumitru (2025) reported verification
through 
. The conjecture is problem 242
in the Erdős problems collection (Bloom 2026).
insbesondere im Falle 
." J. reine angew. Math. 211, 1-10, 1962.Bloom,
T. F. "Erdős Problem 242." Erdős Problems. Oct. 1,
2026. https://www.erdosproblems.com/242.Guy,
R. K. "Egyptian Fractions." §D11 in Unsolved
Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 158-166,
1994.Mihnea, S. and Dumitru, B. C. "Further Verification and
Empirical Evidence for the Erdős-Straus Conjecture." 29 Aug 2025. https://arxiv.org/abs/2509.00128v1.Obláth,
R. "Sur l'equation diophantienne 
." Mathesis 59, 308-316,
1950.Rosati, L. A. "Sull'equazione diofantea 
." Boll. Un. Mat. Ital. 9,
59-63, 1954.Salez, S. E. "The Erdős-Straus Conjecture:
New Modular Equations and Checking up to 
." 24 Jun 2014. https://arxiv.org/abs/1406.6307.Swett,
A. "The Erdos-Strauss Conjecture." Oct. 28, 1999. https://web.archive.org/web/20000110143340/http://math.uindy.edu/swett/esc.htm.Vaughan,
R. C. "On a Problem of Erdős, Straus and Schinzel." Mathematika 17,
193-198, 1970.Wells, D. The
Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England:
Penguin Books, p. 29, 1986.Yamamoto, K. "On the Diophantine
Equation 
."
Mem. Fac. Sci. Kyushu U. Ser. A 19, 37-47, 1965.Weisstein, Eric W. "Erdős-Straus Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Erdos-StrausConjecture.html