31. Then for all positive integers k, the set A contains infinitely many arithmetic progressions of length k. 32. Alternatively, if you add a blue 9, then the blue 1, 5, and 9 are in arithmetic progression . 33. Mr Justice Saied said the " arithmetic progression " for larger amounts than 800 grams should be avoided. 34. :SAy that each of such arithmetic progressions is determined by its first term, and by the increment h. 35. Typical topics include covering system, zero-sum problems, various restricted sumsets, and arithmetic progressions in a set of integers. 36. Fermat also conjectured, and Leonhard Euler proved, that there is no sequence of four squares in arithmetic progression . 37. This can always be achieved by defining " b " to be the first prime in the arithmetic progression . 38. Terence Tao and Ben Green proved in 2005 that there are infinitely many three-term arithmetic progressions of Chen primes. 39. For finite sequences, there exist arbitrarily long arithmetic progressions of primes, a theorem known as the Green Tao theorem. 40. Even the weaker claim that " A " must contain at least one arithmetic progression of length 3 is open.
