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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 |
| Taran Knutson | Michigan A | Louisville A | 22 | 10 |
| Michael Ai | Williams A | Amherst A | 22 | 10 |
| Chris Chang | USC A | UC Irvine | 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 |
| Madeline Strauss | Tufts A | Dartmouth A | 38 | -5 |
| Oliver West | Cambridge B | Cambridge A | 38 | 10 |
| 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 |
| Dawson Teu | Waterloo A | Toronto B | 59 | 10 |
| David Black | Illinois Champaign | Iowa A | 59 | -5 |
| Michael Zheng | UCLA F | UCLA A | 59 | 10 |
| Joseph Wang | UCLA E | Claremont C | 59 | 10 |
| Bharath Ram | Georgia Tech A | Vanderbilt A | 59 | 10 |
| David Xilbille | Georgia Tech C | Alabama A | 59 | 10 |
| Andrew Nucci | UCLA B | UCSD B | 59 | 10 |
| Henry Ding | Princeton | Lehigh B | 59 | 10 |
| Jiping Fang | Illinois Blue | WashU Grizzlers | 59 | 10 |
| Danny Cutbill | RIT A | Binghamton A | 59 | 10 |
| 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 |
| Ellen Ge | Toronto A | Toronto D | 65 | 10 |
| Akif Ismail | Williams C | Brandeis Beethoven | 65 | 10 |
| Salil Jain | Williams B | Boston College A | 67 | 10 |
| James Zhao | Vanderbilt C | Vanderbilt B | 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 |
| Nameer Qadir | Toronto C | McMaster A | 72 | 10 |
| Brendan Bridle | Queen's A | Toronto I | 72 | 10 |
| Saswat Sasha Tripathi | Chicago A | Indiana A | 72 | 10 |
| Ben Mowery | Vermont A | Brandeis Bach | 72 | 10 |
| Daniel Rosado | UCLA D | UCLA C | 72 | 10 |
| Peter Zeng | Ohio State A | Michigan C | 72 | 10 |
| Max Kurzman | UNC D | VCU A | 72 | 10 |
| Anne Fjeld | Alberta A | Washington Pink | 72 | 10 |
| Samarth Prajapati | Georgia Tech E | Tennessee Tech | 72 | 10 |
| Caleb Slusher | South Carolina A | Chipola College | 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 |
| Charlotte Nicholas | Durham B | York | 72 | 10 |
| Rory Moloney | Cambridge E | LSE | 72 | 10 |
| Alex Forman | Cornell D | Binghamton B | 72 | 10 |
| Pace Klein | CWRU B | Michigan State A | 73 | 10 |
| Brody Johnson | Louisville B | Ohio State B | 73 | 10 |
| Arthur Zhang | Purdue C | WashU Grolars | 73 | 10 |
| Gary Wang | Michigan D | Kentucky | 73 | 10 |
| Shivam Saxena | Georgia Tech F | Auburn A | 73 | 10 |
| John Shelley | Clemson B | Sewanne | 73 | -5 |
| Alex Wong | Rutgers D | Stony Brook | 73 | 10 |
| Nayaaz Hashim | Oxford | Bristol | 73 | 10 |
| March Delfin | UCSD A | Claremont B | 74 | 10 |
| Matthew Wozniak | Michigan B | CWRU A | 74 | 10 |
| Yvonne Pan | Amherst B | Southern Connecticut State University A | 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 |
| Joyann Hua | British Columbia B | Washington State | 74 | 10 |
| Kevin Liu | Texas | Arizona State A | 74 | 10 |
| Luke Simon | Alberta B | Washington Chinook | 74 | 10 |
| Eric Morshed | Johns Hopkins | Penn | 74 | 10 |
| James Headon | Edinburgh A | Edinburgh D | 74 | 10 |
| Michael Shipman | Cambridge D | Birmingham | 74 | 10 |
| James Stadler | Imperial B | Imperial A | 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 |
| Sam Alahi | Illinois Orange | Rose-Hulman A | 76 | 10 |
| Jonathan Schnipper | Brandeis Mozart | Brown B | 76 | 10 |
| Justine Hopkins | Liberty C | Liberty B | 76 | 10 |
| Braydon Morefield | George Mason B | Vassar A | 76 | 10 |
| Alex Hestermann | Washington Sockeye | British Columbia A | 76 | 10 |
| George Matsumura | Washington Chum | Washington Steelhead | 76 | 10 |
| Yiwei Jiang | NYU C | George Mason C | 76 | 10 |
| Alex Irvine | Sheffield A | Sheffield 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 |
| Eric Yang | Purdue A | Purdue B | 92 | 10 |
| William Erwin | William & Mary B | Liberty A | 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 |
| Kenner Bailey | Boston University A | Tufts B | 98 | 10 |
| Sewanth Paudel | Ohio State C | Pittsburgh | 98 | 10 |
| James Carrick-Lawson | Southampton | Cardiff | 98 | 10 |
| Austin Embry | Auburn C | Mississippi State A | 111 | 10 |
| Yashaswi Jaishy | Iowa B | Indiana B | 113 | 10 |
| Mason Lambert | JMU A | Duke A | 113 | 10 |
| Grace Early | Iowa A | Illinois Champaign | 116 | 10 |
| Elliott Gomes | Dartmouth A | Tufts A | 116 | 10 |
| Bonham Buchannon | Louisville D | CWRU C | 116 | 10 |
| Ben Kantsiper | JMU B | Tusculum A | 116 | 10 |
| Helen Neves | Boise State | Washington Coho | 116 | 10 |
| Nelson Adams-Riley | Sewanne | Clemson B | 116 | 10 |