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Catalan's Conjecture

Catalan's Conjecture

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Catalan's Conjecture, also known as Mihăilescu's Theorem after the mathematician Preda Mihăilescu who proved it in 2002, is a theorem in number theory that deals with the powers of natural numbers. The conjecture, initially proposed by Eugène Charles Catalan in 1844, states that the equation:

xa - yb = 1

has only one solution in natural numbers ( x, y, a, b ) with both a and b greater than 1. This unique solution is:

32 - 23 = 1

or in terms of the variables in the equation:

x = 3, a = 2, y = 2, b = 3

Catalan conjectured this after observing that there seemed to be no other instances where the difference between two powers of natural numbers is 1. The conjecture was proven to be true by Preda Mihăilescu over 150 years after it was proposed, and hence it is sometimes referred to as Mihăilescu's Theorem. The proof is highly non-trivial and involves sophisticated concepts from algebraic number theory and cyclotomic fields.

The T-Shirt

This t-shirt is everything you've dreamed of and more. It feels soft and lightweight, with the right amount of stretch. It's comfortable and flattering for all.

  • 100% combed and ring-spun cotton
  • Fabric weight: 4.2 oz./yd.² (142 g/m²)
  • Pre-shrunk fabric
  • Side-seamed construction
  • Shoulder-to-shoulder taping
  • Blank product sourced from Nicaragua, Mexico, Honduras, or the US
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