Investigates the ab2 conjecture, exploring its connections between natural numbers and prime numbers, indicating potential mathematical insights.
In this paper, we consider the ab2 conjecture, a proposal concerning the relationship between natural numbers and prime numbers through perfect squares. This conjecture states that for every natural number a>1, there exists a natural number b such thatb<2.32(lna)^2anda+b^2.We present preliminary observations, example tests, and a discussion of the difficulty of finding counterexamples.
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