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On an Elementary Problem in Number Theory
Canadian mathematical bulletin, Tome 1 (1958) no. 1, pp. 5-8

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A question which Chalk and L. Moser asked me several years ago led me to the following problem: Let 0 < x ≤ y. Estimate the smallest f(x) so that there should exist integers u and v satisfying 1 I am going to prove that for every ∊ > 0 there exist arbitrarily large values of x satisfying 2 but that for a certain c > 0 and all x 3 A sharp estimation of f(x) seems to be a difficult problem. It is clear that f(p) = 2 for all primes p. I can prove that f(x)→ ∞ and f(x)/loglog x → 0 if we neglect a sequence of integers of density 0, but I will not give the proof here. 
Erdös, Paul. On an Elementary Problem in Number Theory. Canadian mathematical bulletin, Tome 1 (1958) no. 1, pp. 5-8. doi: 10.4153/CMB-1958-002-9
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