# Arithmetic Progression

1. Jul 1, 2006

### Dragonfall

MATHWORLD: "Erdos offered a prize for a proof of the proposition that 'If the sum of reciprocals of a set of integers diverges, then that set contains arbitrarily long arithmetic progressions.' This conjecture is still open (unsolved), even for 3-term arithmetic progressions. "

What's an n-term arithmetic progression?

Last edited: Jul 1, 2006
2. Jul 1, 2006

### shmoe

Arithmetic progression-consecutive terms differ by a constant amount. x,x+d,x+2*d is a 3 term arithmetic progression, x, x+d, ..., x+(n-1)*d is an n-term arithmetic progression.

Compare Erdos conjecture with Szemeredi's theorem on arithmetic progressions, which makes a stronger assumption about your subset of the integers. Also Green and Tao's result on primes containing arbitrarily long arithmetic progressions as a special case of Erdos conjecture (sum of the reciprocals of the primes diverges)