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min, max (a+c+e) if a+b+c+d+e=1002 pos. integers

Source: 2023 May Olympiad L2 p2

March 24, 2024
number theory

Problem Statement

Let a,b,c,da, b, c, d, and ee be positive integers such that a≤b≤c≤d≤ea\le b\le c\le d\le e and that a+b+c+d+e=1002a+b+c+d+e=1002. a) Determine the largest possible value of a+c+ea+c+e. b) Determine the lowest possible value of a+c+ea+c+e.
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