radical (thing)

The radical of an integer n is defined as the product of the distinct prime numbers that divide n, without repetition. For example, since 8 = 2³:

rad(8) = 2

Or, since 60 = 2² × 3 × 5, we have

rad(60) = 2 × 3 × 5 = 30

This definition is core to the abc conjecture, which states—in broad terms—that given three coprime integers a, b, c that satisfy a + b = c, there are only finitely many such triplets that satisfy

c > rad(abc)^1 + ϵ

For any positive real number ϵ (Epsilon). In other words, the conjecture states broadly that c < rad(abc) with only finitely many exceptions, given the necessary conditions.

See also

• abc conjecture
• relatively prime
• Shinichi Mochizuki
• abc conjecture at Wikipedia
• Sequence A007947—Largest squarefree number dividing n: the squarefree kernel of n, rad(n), radical of n; at The On-Line Encyclopedia of Integer Sequences

Galaxy Song ← Andy’s Brevity Quest 2019 () → Poincaré Conjecture