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The number is not in N-Iran 3rd round-Number Theory 2007

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July 28, 2010
number theory unsolvednumber theory

Problem Statement

Let {ai}i=1∞\{a_i\}_{i=1}^{\infty} be a sequence of positive integers such that a1<a2<a3⋯a_1<a_2<a_3\cdots and all of primes are members of this sequence. Prove that for every n<mn<m 1an+1an+1+⋯+1am∉N\dfrac{1}{a_n} + \dfrac{1}{a_{n+1}} + \cdots + \dfrac{1}{a_m} \not \in \mathbb N
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