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Computation of the Infimum in the Littlewood Conjecture

The famous Littlewood Conjecture states that for any two real numbers , the value is equal to zero. In this article, we provide an algorithm which for given ε > 0 checks if the value is less than ε. In particular with its help, we show that mLC < 1/19. We also provide a similar algorithm for p-adic counterpart of the Littlewood Conjecture and show that an analog of mLC in 2-adic case is at most 1/9.