1

Part of 2024 Tuymaada Olympiad

Problems(2)

Tuymaada 2024 Juniors 1

Source: Tuymaada 2024 Juniors P1

Triangular numbers are numbers of the form

1 + 2 + . . . + n

with positive integer

n

1, 3, 6, 10

, . . . . Find the largest non-triangular positive integer number that cannot be represented as the sum of distinct triangular numbers. Proposed by A. Golovanov

examplesalgebra

divisor of n^4+1

Source: 2024 Tuymaada Senior P1

Prove that a positive integer of the form

n^4 +1

can have more than

1000

divisors of the form

a^4 +1

a

number theoryNT constructionTuymaada