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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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  1. Sourceerdos-problems
  2. StatementRetained
  3. Formal1 retained
  4. Resolutionproved (Lean)
  5. WorkNone recorded
  6. DecisionNone here
  7. The questionNot reached
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Where the source files it575 share a topic
Number Theory576Unit Fractions48
Erdős problem 321accepted
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