Introduction The abc conjecture, independently proposed by Joseph Oesterlé and David Masser in 1985, stands as one of the most profound and unresolved problems in modern number theory. It posits a deep relationship between the additive and multiplicative structures of natural numbers. Specifically, for any three positive integers a , b , c satisfying a + b = c , the conjecture asserts that the product of the distinct prime factors of a b c , denoted rad ( a b c ) , imposes a constraint on the size of c . The core claim is that for any ε > 0 , there exist only finitely many such triples satisfying: c > rad ( a b c ) 1 + ε This paper attempts to reinterpret the abc conjecture through the lens of the author’s original “prime geometry model.” This model visualizes prime numbers not as isolated points on the number line, but as rays or line bundles in space, allowing number-theoretic structures to be understood geometrically. By applying this model, we aim to offer new geometri...
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