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Writing a positive integer as sum of two terms of sequence.

Source: ILL 1979-52

June 5, 2011

number theory unsolvednumber theory

Problem Statement

Let a real number

\lambda > 1

be given and a sequence

(n_k)

of positive integers such that

\frac{n_{k+1}}{n_k}> \lambda

for

k = 1, 2,\ldots

Prove that there exists a positive integer

c

such that no positive integer

n

can be represented in more than

c

ways in the form

n = n_k + n_j

or

n = n_r - n_s

.

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