Some Problems on Number Theory

  title={Some Problems on Number Theory},
  author={Paul Erd{\"o}s},
A k = max(p,+ t p,), k < p, < p, + , < 2k . In fact I cannot even disprove f(k) = Ak for all sufficiently large k, though it seems likely that f(k) > Ak for all large k. A well known theorem of Pólya and Störmer states that if u > uo(k) then u(u + 1) always contains a prime factor greater than k, thusf(k) can be determined in a finite number of steps, and an explicit bound has been given by Lehmer (1964) for the number of necessary steps. It is known (Utz, 1961) that f(2) = 2,f(3) =f(4) = 3, f… CONTINUE READING