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Omni-MATH / Let S is the set of prime numbers that less or equal to 26. Is there any a₁,a₂,a₃,a₄,a₅,a₆∈N such that gcd(a_(i),a_(j))∈S for 1≤i≠j≤6 and for every element p of S there exists a pa…

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problem

Let S\mathbb{S} is the set of prime numbers that less or equal to 26. Is there any a1,a2,a3,a4,a5,a6∈Na_1, a_2, a_3, a_4, a_5, a_6 \in \mathbb{N} such that gcd(ai,aj)∈Sfor 1≤i≠j≤6 gcd(a_i,a_j) \in \mathbb{S} \qquad \text {for } 1\leq i \ne j \leq 6 and for every element pp of S\mathbb{S} there exists a pair of 1≤k≠l≤6 1\leq k \ne l \leq 6 such that $$s=gcd(a_k,a_l)?$$
Plain-text mathematical notation (without MathML)
Let S is the set of prime numbers that less or equal to 26. Is there any a₁,a₂,a₃,a₄,a₅,a₆∈N such that gcd(a_(i),a_(j))∈S for 1≤i≠j≤6 and for every element p of S there exists a pair of 1≤k≠l≤6 such that $$s=gcd(a_k,a_l)?$$
Original LaTeX notation
Let $\mathbb{S}$ is the set of prime numbers that less or equal to 26. Is there any $a_1, a_2, a_3, a_4, a_5, a_6 \in \mathbb{N}$ such that $$ gcd(a_i,a_j) \in \mathbb{S} \qquad \text {for }  1\leq i \ne j \leq 6$$ and for every element $p$ of $\mathbb{S}$ there exists a pair of $ 1\leq k \ne l \leq 6$ such that $$s=gcd(a_k,a_l)?$$

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task_id
568c007c-dce8-5b9e-b406-e07b8d7dd94a
task_key
test--568c007c-dce8-5b9e-b406-e07b8d7dd94a
task_revision_id
1
config / split
/ test

Official source

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