In arithmetic combinatorics, the Erdős–Szemerédi theorem states that for every finite set A of integers, at least one of the sets A + A and A · A (the sets of pairwise sums and pairwise products, respectively) form a significantly larger set. More precisely, the Erdős–Szemerédi theorem states that there exist positive constants c and ε such that, for any non-empty set A ⊂ ℕ, max ( | A + A | , | A ⋅ A | ) ≥ c | A | 1 + ε .
In arithmetic combinatorics, the Erdős–Szemerédi theorem states that for every finite set A of integers, at least one of the sets A + A and A · A (the sets of pairwise sums and pairwise products, respectively) form a significantly larger set. More precisely, the Erdős–Szemerédi theorem states that there exist positive constants c and ε such that, for any non-empty set A ⊂ ℕ, max ( | A + A | , | A ⋅ A | ) ≥ c | A | 1 + ε .
Source: Wikipedia "Erdős–Szemerédi theorem" · CC BY-SA 4.0
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