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An ideal of a ring can be described by this adjective if and only if its associated quotient ring is an integral domain. If the characteristic of a field is non-zero, it is a number described by this adjective. An integer is raised to the power of a number described by this adjective in the statement of Fermat’s Little Theorem. Two integers whose highest common factor is one are said to be “co-,” or “relatively,” this adjective. The Fundamental Theorem of Arithmetic states that each integer greater than one can be factored uniquely into numbers described by this adjective. For 10 points, give this adjective used to describe numbers whose only factors are themselves and one. ■END■
| Upstate NY | Main | Y | 5 | 100% | 0% | 0% | 67.80 |
| Eastern Canada (2) | Main | Y | 9 | 100% | 0% | 0% | 66.00 |
| Great Lakes | Main | Y | 12 | 92% | 0% | 17% | 76.82 |
| Lower Mid-Atlantic | Main | Y | 6 | 100% | 0% | 0% | 94.00 |
| Upper Mid-Atlantic | Main | Y | 12 | 100% | 0% | 0% | 67.75 |
| Midwest | Main | Y | 9 | 100% | 0% | 33% | 83.44 |
| Northeast | Main | Y | 12 | 100% | 0% | 8% | 67.00 |
| Pacific | Main | Y | 9 | 100% | 0% | 11% | 75.56 |
| Southeast | Main | Y | 12 | 100% | 0% | 17% | 79.58 |
| Southern California | Main | Y | 7 | 100% | 0% | 14% | 55.14 |
| UK (South) | UK | Y | 8 | 100% | 0% | 0% | 71.50 |
| UK (North) | UK | Y | 5 | 100% | 0% | 20% | 72.20 |
| Player | Team | Opponent | Buzz Position | Value |
|---|---|---|---|---|
| Tal Bowen | Durham A | Durham C | 16 | -5 |
| Oliver Thompson | CWRU D | Michigan State B | 18 | -5 |
| Rishi Mathur | Claremont B | UCSD A | 21 | -5 |
| Chris Chang | USC A | UC Irvine | 22 | 10 |
| Taran Knutson | Michigan A | Louisville A | 22 | 10 |
| Michael Ai | Williams A | Amherst A | 22 | 10 |
| Beckett Pursey | Purdue B | Purdue A | 25 | -5 |
| Daniel Abrams | Rutgers B | Columbia A | 28 | 10 |
| Skand Parvatikar | Arizona State B | British Columbia C | 34 | 10 |
| Sidarth Erat | MIT A | Dartmouth B | 35 | 10 |
| Nate Brown | CWRU C | Louisville D | 38 | -5 |
| Oliver West | Cambridge B | Cambridge A | 38 | 10 |
| Madeline Strauss | Tufts A | Dartmouth A | 38 | -5 |
| Annika Larson | Claremont A | UC Santa Barbara | 41 | 10 |
| Eli Zimmerman | Tufts C | Boston College B | 42 | 10 |
| Platon Gorokhov | Toronto E | Waterloo C | 45 | 10 |
| Eric Lipsutz | Chicago B | William Woods University A | 50 | -5 |
| Daniel Chen | Emory A | Georgia Tech B | 52 | -5 |
| Imtiaz Kidwai | Toronto F | Brock A | 58 | 10 |
| Andrew Nucci | UCLA B | UCSD B | 59 | 10 |
| Dawson Teu | Waterloo A | Toronto B | 59 | 10 |
| Henry Ding | Princeton | Lehigh B | 59 | 10 |
| Jiping Fang | Illinois Blue | WashU Grizzlers | 59 | 10 |
| Bharath Ram | Georgia Tech A | Vanderbilt A | 59 | 10 |
| David Xilbille | Georgia Tech C | Alabama A | 59 | 10 |
| Danny Cutbill | RIT A | Binghamton A | 59 | 10 |
| Michael Zheng | UCLA F | UCLA A | 59 | 10 |
| Joseph Wang | UCLA E | Claremont C | 59 | 10 |
| David Black | Illinois Champaign | Iowa A | 59 | -5 |
| Derek Li | Cornell A | RIT B | 60 | 10 |
| Pen Hughes | Edinburgh C | Edinburgh B | 61 | 10 |
| Eames Weeks | Brown A | Vermont B | 62 | 10 |
| Gabe Rosen-Turits | NYU B | Lehigh A | 62 | 10 |
| Logan Van Pelt | Washington Coho | Boise State | 64 | -5 |
| Akif Ismail | Williams C | Brandeis Beethoven | 65 | 10 |
| Ellen Ge | Toronto A | Toronto D | 65 | 10 |
| James Zhao | Vanderbilt C | Vanderbilt B | 67 | 10 |
| Salil Jain | Williams B | Boston College A | 67 | 10 |
| Jason Lee | Rutgers A | NYU A | 68 | 10 |
| Harry Oxley | Imperial C | Imperial D | 69 | 10 |
| Sicheng Jiang | Toronto H | McMaster C | 71 | 10 |
| Daniel Huang | Georgia Tech D | Clemson C | 71 | 10 |
| Brendan Bridle | Queen's A | Toronto I | 72 | 10 |
| Ben Mowery | Vermont A | Brandeis Bach | 72 | 10 |
| Samarth Prajapati | Georgia Tech E | Tennessee Tech | 72 | 10 |
| Caleb Slusher | South Carolina A | Chipola College | 72 | 10 |
| Rory Moloney | Cambridge E | LSE | 72 | 10 |
| Nameer Qadir | Toronto C | McMaster A | 72 | 10 |
| Peter Zeng | Ohio State A | Michigan C | 72 | 10 |
| Max Kurzman | UNC D | VCU A | 72 | 10 |
| Rohit Chintala | Maryland B | Maryland C | 72 | 10 |
| Cooper Morris | Columbia B | Vassar B | 72 | 10 |
| Ba Loc Dinh | Illinois Urbana | Illinois Canada | 72 | 10 |
| Anne Fjeld | Alberta A | Washington Pink | 72 | 10 |
| Charlotte Nicholas | Durham B | York | 72 | 10 |
| Alex Forman | Cornell D | Binghamton B | 72 | 10 |
| Daniel Rosado | UCLA D | UCLA C | 72 | 10 |
| Saswat Sasha Tripathi | Chicago A | Indiana A | 72 | 10 |
| Pace Klein | CWRU B | Michigan State A | 73 | 10 |
| Brody Johnson | Louisville B | Ohio State B | 73 | 10 |
| Shivam Saxena | Georgia Tech F | Auburn A | 73 | 10 |
| John Shelley | Clemson B | Sewanne | 73 | -5 |
| Nayaaz Hashim | Oxford | Bristol | 73 | 10 |
| Gary Wang | Michigan D | Kentucky | 73 | 10 |
| Alex Wong | Rutgers D | Stony Brook | 73 | 10 |
| Arthur Zhang | Purdue C | WashU Grolars | 73 | 10 |
| Matthew Wozniak | Michigan B | CWRU A | 74 | 10 |
| Kevin Liu | Texas | Arizona State A | 74 | 10 |
| Luke Simon | Alberta B | Washington Chinook | 74 | 10 |
| Michael Shipman | Cambridge D | Birmingham | 74 | 10 |
| James Stadler | Imperial B | Imperial A | 74 | 10 |
| March Delfin | UCSD A | Claremont B | 74 | 10 |
| Ryan Liu | Ohio State D | Michigan State D | 74 | 10 |
| Josue Lopez | WVU A | Louisville C | 74 | 10 |
| Kevin Liu | Maryland A | George Mason A | 74 | 10 |
| Eric Morshed | Johns Hopkins | Penn | 74 | 10 |
| Yvonne Pan | Amherst B | Southern Connecticut State University A | 74 | 10 |
| Joyann Hua | British Columbia B | Washington State | 74 | 10 |
| James Headon | Edinburgh A | Edinburgh D | 74 | 10 |
| Jolie Yeh | Warwick | Cambridge C | 74 | 10 |
| Gregory Stone | ESF | Binghamton C | 74 | 10 |
| Gabriel Nell | Cornell B | Cornell C | 74 | 10 |
| William Berger | Dartmouth C | MIT B | 75 | 10 |
| Aleksa Misic | Waterloo B | Guelph A | 76 | 10 |
| Liam Henderson | McMaster B | Toronto G | 76 | 10 |
| George Matsumura | Washington Chum | Washington Steelhead | 76 | 10 |
| Justine Hopkins | Liberty C | Liberty B | 76 | 10 |
| Braydon Morefield | George Mason B | Vassar A | 76 | 10 |
| Yiwei Jiang | NYU C | George Mason C | 76 | 10 |
| Alex Hestermann | Washington Sockeye | British Columbia A | 76 | 10 |
| Alex Irvine | Sheffield A | Sheffield B | 76 | 10 |
| Sam Alahi | Illinois Orange | Rose-Hulman A | 76 | 10 |
| Jonathan Schnipper | Brandeis Mozart | Brown B | 76 | 10 |
| Alex Dzurick | William Woods University A | Chicago B | 78 | 10 |
| Rafa Travis | Durham C | Durham A | 78 | 10 |
| Wesley Stine | Clemson A | Tennessee A | 79 | 10 |
| Aryan Malhotra | Rutgers C | Rowan | 79 | 10 |
| Coy Mier | Auburn B | Georgia A | 83 | 10 |
| Stella Brown | Washington Masu | Washington Atlantic | 84 | 10 |
| William Erwin | William & Mary B | Liberty A | 92 | 10 |
| Eric Yang | Purdue A | Purdue B | 92 | 10 |
| Louis Harney | Georgia Tech B | Emory A | 93 | 10 |
| Antonio LaNave | Virginia Tech C | UNC B | 95 | 10 |
| Pratham Bhanushali | WVU B | Michigan State C | 96 | 10 |
| James Carrick-Lawson | Southampton | Cardiff | 98 | 10 |
| Sewanth Paudel | Ohio State C | Pittsburgh | 98 | 10 |
| Kenner Bailey | Boston University A | Tufts B | 98 | 10 |
| Austin Embry | Auburn C | Mississippi State A | 111 | 10 |
| Mason Lambert | JMU A | Duke A | 113 | 10 |
| Yashaswi Jaishy | Iowa B | Indiana B | 113 | 10 |
| Nelson Adams-Riley | Sewanne | Clemson B | 116 | 10 |
| Bonham Buchannon | Louisville D | CWRU C | 116 | 10 |
| Ben Kantsiper | JMU B | Tusculum A | 116 | 10 |
| Elliott Gomes | Dartmouth A | Tufts A | 116 | 10 |
| Helen Neves | Boise State | Washington Coho | 116 | 10 |
| Grace Early | Iowa A | Illinois Champaign | 116 | 10 |