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Indecomposable Numbers in the set V - [ILL 1977]

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January 11, 2011
number theory proposednumber theory

Problem Statement

Let pp be a prime number greater than 5.5. Let VV be the collection of all positive integers nn that can be written in the form n=kp+1n = kp + 1 or n=kp−1 (k=1,2,…).n = kp - 1 \ (k = 1, 2, \ldots). A number n∈Vn \in V is called indecomposable in VV if it is impossible to find k,l∈Vk, l \in V such that n=kl.n = kl. Prove that there exists a number N∈VN \in V that can be factorized into indecomposable factors in VV in more than one way.
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