2

Part of 2016 Finnish National High School Mathematics Comp

Problems(1)

y in a 9-digit base system, is a triangular number,

Source: Finland 2016, Problem 2

y

is a positive integer written only with digit

1

9

system. Prove that

y

is a triangular number, that is, exists positive integer

n

such that the number

y

is the sum of the

n

natural numbers from

1

n

number baseTriangular numberNumerical systemsnumber theoryalgebra