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2003 KJMO P5 remainder always 1

Source: 2003 KJMO P5

June 29, 2024
number theoryKJMOIntegers

Problem Statement

Four odd positive intgers a,b,c,d(a≤b≤c≤d)a, b, c, d (a\leq b \leq c\leq d) are given. Choose any three numbers among them and divide their sum by the un-chosen number, and you will always get the remainder as 11. Find all (a,b,c,d)(a, b, c, d) that satisfies this.
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