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Omni-MATH / Number a is such that ∀a₁,a₂,a₃,a₄∈R, there are integers k₁,k₂,k₃,k₄ such that ∑_(1≤i<j≤4)((a_(i)−k_(i))−(a_(j)−k_(j)))²≤a. Find the minimum of a.

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problem

Number aa is such that a1,a2,a3,a4R\forall a_1, a_2, a_3, a_4 \in \mathbb{R}, there are integers k1,k2,k3,k4k_1, k_2, k_3, k_4 such that 1i<j4((aiki)(ajkj))2a\sum_{1 \leq i < j \leq 4} ((a_i - k_i) - (a_j - k_j))^2 \leq a. Find the minimum of aa.
Plain-text mathematical notation (without MathML)
Number a is such that ∀a₁,a₂,a₃,a₄∈R, there are integers k₁,k₂,k₃,k₄ such that ∑_(1≤i<j≤4)((a_(i)−k_(i))−(a_(j)−k_(j)))²≤a. Find the minimum of a.
Original LaTeX notation
Number $a$ is such that $\forall a_1, a_2, a_3, a_4 \in \mathbb{R}$, there are integers $k_1, k_2, k_3, k_4$ such that $\sum_{1 \leq i < j \leq 4} ((a_i - k_i) - (a_j - k_j))^2 \leq a$. Find the minimum of $a$.

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