MathDB
a%b + a%2b + a%3b + ... + a%nb = a + b

Source: AIMO 2007, TST 6, P1

January 11, 2009
algebra unsolvedalgebra

Problem Statement

For a multiple of kb kb of b b let a%kb a \% kb be the greatest number such that a \% kb \equal{} a \bmod b which is smaller than kb kb and not greater than a a itself. Let n \in \mathbb{Z}^ \plus{} . Determine all integer pairs (a,b) (a,b) with: a\%b \plus{} a\%2b \plus{} a\%3b \plus{} \ldots \plus{} a\%nb \equal{} a \plus{} b
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