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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 |
| 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 |
| Michael Zheng | UCLA F | UCLA A | 59 | 10 |
| Joseph Wang | UCLA E | Claremont C | 59 | 10 |
| Dawson Teu | Waterloo A | Toronto B | 59 | 10 |
| David Black | Illinois Champaign | Iowa A | 59 | -5 |
| 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 |
| Andrew Nucci | UCLA B | UCSD B | 59 | 10 |
| Henry Ding | Princeton | Lehigh B | 59 | 10 |
| Jiping Fang | Illinois Blue | WashU Grizzlers | 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 |
| Akif Ismail | Williams C | Brandeis Beethoven | 65 | 10 |
| Ellen Ge | Toronto A | Toronto D | 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 |
| Peter Zeng | Ohio State A | Michigan C | 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 |
| Daniel Rosado | UCLA D | UCLA C | 72 | 10 |
| Nameer Qadir | Toronto C | McMaster A | 72 | 10 |
| Brendan Bridle | Queen's A | Toronto I | 72 | 10 |
| Max Kurzman | UNC D | VCU A | 72 | 10 |
| Saswat Sasha Tripathi | Chicago A | Indiana A | 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 |
| 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 |
| Pace Klein | CWRU B | Michigan State A | 73 | 10 |
| Brody Johnson | Louisville B | Ohio State B | 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 |
| Nayaaz Hashim | Oxford | Bristol | 73 | 10 |
| Alex Wong | Rutgers D | Stony Brook | 73 | 10 |
| Arthur Zhang | Purdue C | WashU Grolars | 73 | 10 |
| March Delfin | UCSD A | Claremont B | 74 | 10 |
| Matthew Wozniak | Michigan B | CWRU A | 74 | 10 |
| Ryan Liu | Ohio State D | Michigan State D | 74 | 10 |
| Josue Lopez | WVU A | Louisville C | 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 |
| Kevin Liu | Maryland A | George Mason 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 |
| Eric Morshed | Johns Hopkins | Penn | 74 | 10 |
| Yvonne Pan | Amherst B | Southern Connecticut State University A | 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 |
| George Matsumura | Washington Chum | Washington Steelhead | 76 | 10 |
| Aleksa Misic | Waterloo B | Guelph A | 76 | 10 |
| Liam Henderson | McMaster B | Toronto G | 76 | 10 |
| Justine Hopkins | Liberty C | Liberty B | 76 | 10 |
| Braydon Morefield | George Mason B | Vassar A | 76 | 10 |
| Sam Alahi | Illinois Orange | Rose-Hulman A | 76 | 10 |
| Jonathan Schnipper | Brandeis Mozart | Brown B | 76 | 10 |
| Alex Hestermann | Washington Sockeye | British Columbia A | 76 | 10 |
| Alex Irvine | Sheffield A | Sheffield B | 76 | 10 |
| Yiwei Jiang | NYU C | George Mason C | 76 | 10 |
| Rafa Travis | Durham C | Durham A | 78 | 10 |
| Alex Dzurick | William Woods University A | Chicago B | 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 |
| Sewanth Paudel | Ohio State C | Pittsburgh | 98 | 10 |
| James Carrick-Lawson | Southampton | Cardiff | 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 |
| Bonham Buchannon | Louisville D | CWRU C | 116 | 10 |
| Nelson Adams-Riley | Sewanne | Clemson B | 116 | 10 |
| Ben Kantsiper | JMU B | Tusculum A | 116 | 10 |
| Grace Early | Iowa A | Illinois Champaign | 116 | 10 |
| Helen Neves | Boise State | Washington Coho | 116 | 10 |
| Elliott Gomes | Dartmouth A | Tufts A | 116 | 10 |