, Volume 11, Issue 2, pp 212-216

On a conjecture by Erdös-Straus

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Abstract

Two algorithms have been constructed. The first is intended for obtaining such residue-classes represented by the numberN to the given modulusM, that for the primenN (modM) equation (1) is solvable in natural numbersx,y,z. Particularly, whenM=120120 (see Table 2) we obtain 198 suchN, i.e. the hypothesis indicated below is true with a probability greater than 0.99835. The second algorithm is intended for testing the conjecture by Erdös-Straus when 107 <n≦108.