M2669

Part of Kvant 2021

Problems(1)

Groups with sum equal to a power of three

Source: Kvant Magazine No. 9 2021 M2669

Prove that for any natural number

n{}

1,2,\ldots,n

can be divided into several groups so that the sum of the numbers in each group is equal to a power of three.
Proposed by V. Novikov

number theoryKvant