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Erdős problem 290

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Let a≥1a\geq 1. Must there exist some b>ab>a such that ∑a≤n≤b1n=r1s1 and ∑a≤n≤b+11n=r2s2,\sum_{a\leq n\leq b}\frac{1}{n}=\frac{r_1}{s_1}\textrm{ and } \sum_{a\leq n\leq b+1}\frac{1}{n}=\frac{r_2}{s_2}, with (ri,si)=1(r_i,s_i)=1 and s2<s1s_2<s_1? If so, how does this b(a)b(a) grow with aa?

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Problem row
sha256:4889c1581850ee6d06e113144cdc939ec8f7bd1e92ffcc5be9203f6091536ea1
Metadata
sha256:d9d6a704a03b9982298de5d7bd805d9be5bef1758bcfe7a4b479ea0091caa22c
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:6678ce3bef035129ab589425019acc9945683801931f2e9ed5995e62ce3a723a
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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