MathDB

35

Part of 1974 IMO Longlists

Problems(1)

Determine the maximum value of b - a [ILL 1974]

Source:

1/2/2011
If pp and qq are distinct prime numbers, then there are integers x0x_0 and y0y_0 such that 1=px0+qy0.1 = px_0 + qy_0. Determine the maximum value of b−ab - a, where aa and bb are positive integers with the following property: If a≤t≤ba \leq t \leq b, and tt is an integer, then there are integers xx and yy with 0≤x≤q−10 \leq x \leq q - 1 and 0≤y≤p−10 \leq y \leq p - 1 such that t=px+qy.t = px + qy.
number theoryprime numbersnumber theory proposed