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Number theory - Iran

Source: Iran MO 2017 - 2nd Round - P1

April 20, 2017
number theoryprime numbers

Problem Statement

a) Prove that there doesn't exist sequence a1,a2,a3,...∈Na_1,a_2,a_3,... \in \mathbb{N} such that: ∀i<j:gcd(ai+j,aj+i)=1\forall i<j: gcd(a_i+j,a_j+i)=1
b) Let pp be an odd prime number. Prove that there exist sequence a1,a2,a3,...∈Na_1,a_2,a_3,... \in \mathbb{N} such that: ∀i<j:p∤gcd(ai+j,aj+i)\forall i<j: p \not | gcd(a_i+j,a_j+i)
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