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a+b = 1. Show that c+d = 1 iff [na]+[nb] = [nc]+[nd] for all n

Source: Polish second round 1995 p3

January 19, 2020
irrationalfloor functionalgebra

Problem Statement

Let a,b,c,da,b,c,d be positive irrational numbers with a+b=1a+b = 1. Show that c+d=1c+d = 1 if and only if [na]+[nb]=[nc]+[nd][na]+[nb] = [nc]+[nd] for all positive integers nn.
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