arithmetic sequences - 2024 ACF Winter at Online

Question

Salem–Spencer sets cannot contain any non-trivial examples of these sequences, which are the subject of Szemerédi's theorem. For 10 points each:

[10e] Name these sequences in which the difference between any two consecutive terms is constant, unlike in geometric sequences.

ANSWER: arithmetic sequences [or arithmetic progressions]

[10h] In 2004, Szemerédi's theorem was extended with this result, which states that the sequence of prime numbers contains arbitrarily long arithmetic sequences.

ANSWER: Green–Tao theorem

[10m] The Green–Tao theorem led to improved results concerning the first Hardy–Littlewood conjecture, which generalizes this conjecture. This conjecture has been verified up to 10-to-the-388342, somewhat larger than the 10-to-the-18 upper bound for Goldbach’s conjecture.

ANSWER: twin prime conjecture

Back to bonuses

Summary


2024 ACF Winter at UC Berkeley	2024-11-16	Y	3	20.00	100%	33%	67%
2024 ACF Winter at Clemson	2024-11-16	Y	7	14.29	100%	14%	29%
2024 ACF Winter at Lehigh	2024-11-16	Y	7	15.71	100%	14%	43%
2024 ACF Winter at Northwestern	2024-11-16	Y	9	17.78	100%	33%	44%
2024 ACF Winter at Ohio State	2024-11-16	Y	6	13.33	100%	17%	17%
2024 ACF Winter at Online	2024-11-16	Y	7	12.86	100%	29%	0%
2024 ACF Winter at UBC	2024-11-16	Y	2	25.00	100%	100%	50%
2024 ACF Winter at Central Florida	2024-11-16	Y	5	12.00	100%	0%	20%
2024 ACF Winter at Oxford	2024-11-16	Y	10	14.00	100%	30%	10%
2024 ACF Winter at Brandeis	2024-11-16	Y	8	17.50	100%	50%	25%

Data


Vassar B	Colorado College	10	0	10
Texas B	McGill E	10	10	20
Missouri	NYU B	10	0	10
NYU A	Vassar A	10	0	10
Texas A	Mississippi State	10	10	20
Texas C	Oregon State	10	0	10
WUSTL A	Iowa	10	0	10