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a_i, i=1,...,7 consist of the numbers 1,...,7 ifsum 3^{a_i} = 6558

Source: 1984 Swedish Mathematical Competition p6

March 28, 2021
Sumcombinatoricsnumber theory

Problem Statement

Assume a1,a2,...,a14a_1,a_2,...,a_{14} are positive integers such that ∑i=1143ai=6558\sum_{i=1}^{14}3^{a_i} = 6558. Prove that the numbers a1,a2,...,a14a_1,a_2,...,a_{14} consist of the numbers 1,...,71,...,7, each taken twice.
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