Geodesic
On a Theorem of Rav Concerning Egyptian Fractions
Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 155-156

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Problems involving Egyptian fractions (rationals whose numerator is 1 and whose denominator is a positive integer) have been extensively studied. (See [1] for a more complete bibliography). Some of the most interesting questions, many still unsolved, concern the solvability of where k is fixed.In [2] Rav proved necessary and sufficient conditions for the solvabilty of the above equation, as a consequence of some other theorems which are rather complicated in their proofs. In this note we give a short, elementary proof of this theorem, and at the same time generalize it slightly. 
Webb, William A. On a Theorem of Rav Concerning Egyptian Fractions. Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 155-156. doi: 10.4153/CMB-1975-031-5
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[1] 1. Bleicher, M. N., A new algorithm for the expansion of Egyptian fractions, J. of Number Theory, Vol. 4 (1972), 342-382. Google Scholar

[2] 2. Rav, Y., On the representation of a rational number as a sum of a fixed number of unit fractions, J. Reine Angew. Math. 222 (1966), 207-213. Google Scholar

[3] 3. Stewart, B. M. and Webb, W. A., Sums of fractions with bounded numerators, Can. J. Math., 18 (1966), 999-1003. Google Scholar

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