Shinichi Mochizuki, a mathematician at Kyoto University in Japan, has released a 500-page proof of the “abc” conjecture, a celebrated unsolved problem originally posed in 1985.
Let sqp(n) denote the square-free part of an integer n, or in other words the product of the prime factors of n. For example, sqp(18) = 2 * 3 = 6 (here * denotes multiplication). The abc conjecture asserts that for integers a, b and c, where a + b = c, the ratio sqp(a*b*c)r/c always has some minimum value greater than zero for any value of r greater than 1. For example, if
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