MathDB

279

Part of 1979 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 279 All Soviet Union MO 1979 divide [0,1] onto (p+q) equal segments

Source:

7/14/2019
Natural pp and qq are relatively prime. The [0,1][0,1] is divided onto (p+q)(p+q) equal segments. Prove that every segment except two marginal contain exactly one from the (p+q−2)(p+q-2) numbers {1/p,2/p,...,(p−1)/p,1/q,2/q,...,(q−1)/q}\{1/p, 2/p, ... , (p-1)/p, 1/q, 2/q, ... , (q-1)/q\}
combinatoricsequal segmentsnumber theoryrelatively prime