Warning: mysql_numrows(): supplied argument is not a valid MySQL result resource in /home/kidsnetau/encyclopedia_content.txt on line 11

## Encyclopedia > Catalan's conjecture

Article Content

# Catalan's conjecture

Catalan's conjecture is a simple conjecture in number theory that was proposed by the mathematician Eugène Charles Catalan[?].

To understand the conjecture notice that 23 = 8 and 32 = 9 are two consecutive powers of natural numbers. Catalan's conjecture states that this is the only case of two consecutive powers.

That is to say, Catalan's conjecture states that the only solution in the natural numbers of

xa − yb = 1
for x,a,y,b > 1 is x = 3, a = 2, y = 2, b = 3.

In particular, notice that it's unimportant that the same numbers 2 and 3 are repeated in the equation 32 − 23 = 1. Even a case where the numbers were not repeated would still be a counterexample to Catalan's conjecture.

A proof of Catalan's conjecture, which would make it a theorem, was claimed by the mathematician Preda Mihailescu[?] in April 2002. The proof is still being checked.

External links:

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia
 Search over one million articles, find something about almost anything!

Featured Article
 List of Swiss people ... (1530-1576), theologian, historian Rudolf Steiner, (1861-1925), mystic, philosopher and educator Philippe Suchard[?] (1797-1884), chocolatier John Sutter (1803-1880), ...