square - 2024 PACE NSC - Buzzpoints App

Question

The [emphasize] inverse of this function bounds the magnitude of the Mertens function in the disproven Mertens conjecture. If there exists an integer n for which this function of n equals q mod p, then the Legendre symbol of q over p equals one. This (20[1])function is applied to y when defining an elliptic curve. The Möbius (20[1])function is non-zero (20[1])for numbers that are (*) “free” (10[1])of this (10[1])function, meaning (10[1])that (10[1])their prime factorizations contain no repeats. (10[2])Replacing (10[1])this function (10[2])with any higher-order analog causes (10[1])an equation (10[3])with (10[2])infinite solutions (10[1])to have (10[1])no solutions via Fermat’s last (10[1])theorem. This function (10[1])and (10[1])addition define Pythagorean (10[1])triplets. (10[4])For 10 points, name this (10[1])function (10[1])that multiplies (10[1])a (10[1])number (10[1])by (10[1])itself. (10[1])■END■ (10[7])

ANSWER: square [accept word forms like squaring and squared; accept power two; accept answers indicating exponentiation with exponent two, like second power; reject answers indicating that two is the base, like “power of two” or “two to the power of n”]

= Average correct buzz position

Back to tossups

Buzzes

Player	Team	Opponent	Buzz Position	Value
Kevin Wang	Johns Creek A	University Lab	44	20
Jacob Goldman-Wetzler	Hastings	Johns Creek A	56	20
Hayden Qi	Johns Creek B	Northmont A	59	20
Ali Hamzeh	Kinkaid	Heights	64	10
Sohum Sukhatankar	St. Mark's	University Lab	66	10
Robert Wang	Livingston A	Richard Montgomery A	68	10
Hazel DePreist-Sullivan	Hastings	St. Mark's	69	10
Rishabh Mahale	Okemos	Solon	75	10
Andrew Li	Winston Churchill B	West Point	75	10
Landon Block	Owensboro	Hoover B	76	10
Krish Chinta	Innovation Academy A	Heights	78	10
Tejas Kohli	Lambert	Winston Churchill A	78	10
Angela Sun	Solon	Chattahoochee	83	10
Rohan Kher	Barrington	Hunter A	85	10
Alex Zhang	Okemos	Detroit Catholic Central C	85	10
Ryan McKenzie	McLean A	Seven Lakes	85	10
Abigail AuYeung	DuPage County AT	Winston Churchill B	86	10
Brodie Henry	West Point	Hunter B	86	10
Spencer Thomas	Durham AT	Innovation Academy B	88	10
Sky Hong	Choate Rosemary Hall	Fairfield County AT	90	10
Jacob Barta	Detroit Catholic Central A	Walter Payton A	95	10
Matthew Wozniak	Freeman	Carl Sandburg	98	10
Clete Reinberger	Cincinnati Hills	James W. Robinson	99	10
Alex Xu	Canyon Crest	Strake Jesuit	102	10
Keefer Lin	Chattahoochee	Detroit Catholic Central C	103	10
Thomas Belcher	Saint Joseph	Elkhorn North	103	10
Omkar Marathe	William Fremd	Great Valley	103	10
Timothy Porter	Maggie Walker A	Thomas Jefferson D	103	10
Ben Hellman	Georgetown Day	Livingston B	108	10
Romir Mukherjee	Hunter B	DuPage County AT	109	10
Aaron Lin	McLean B	Northmont B	111	10
Natalija Ducich	Lightridge	Downingtown STEM	112	10
Myles Breguet	Norfolk Academic Guild	Maggie Walker C	113	10
Ryan Dai	Carbondale	Detroit Catholic Central B	114	10
Jonathan Tao	Stevenson B	Maggie Walker B	115	10
Fern Fang	McLean A	Alabama Cyber Tech	116	10
Aditya Patnaik	Beavercreek	Mexico	116	10
Thomas Glotfelty	James W. Robinson	Walter Payton B	116	10
Jingyi Wu	Stevenson A	Lindbergh	116	10
Ozan Demiroglu	Seven Lakes	Richard Montgomery B	116	10
Clete Reinberger	Cincinnati Hills	St. Xavier	116	10
Alan Fan	Thomas Jefferson C	Thomas Jefferson B	116	10

Summary

Tournament	Edition	Exact Match?	TUH	Conv. %	Power %	Neg %	Average Buzz
2024 PACE NSC	06/08/2024	Y	42	100%	7%	0%	92.76