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Junior Balkan Mathematical Olympiad 2021- P2

Source: JBMO 2021

July 1, 2021

JuniorBalkannumber theorySetsmaximum

Problem Statement

For any set

A = \{x_1, x_2, x_3, x_4, x_5\}

of five distinct positive integers denote by

S_A

the sum of its elements, and denote by

T_A

the number of triples

(i, j, k)

with

1 \le i < j < k \le 5

for which

x_i + x_j + x_k

divides

S_A

. Find the largest possible value of

T_A

.

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