Question
Sometimes, division by 648 is actually multiplication by 12. Answer the following about modular arithmetic, for 10 points each.
[10m] This theorem ensures that for a system of integer congruences each of the form “x is congruent to a-sub-i mod n-sub-i,” there is always an integer solution.
ANSWER: Chinese remainder theorem [accept CRT]
[10h] The Chinese remainder theorem generalizes to rings by replacing the moduli with these sets and coprimality with comaximality. Two of these things are comaximal if 1 can be written as a sum of elements chosen from them.
ANSWER: ideals [accept pairwise comaximal ideals]
[10e] To actually solve a system of integer congruences, one uses repeated division in Euclid’s algorithm for computing this function. Two integers are coprime if this function returns 1 when applied to them.
ANSWER: greatest common divisor [accept greatest common factor or gcd or gcf]
<RA, Other Science: Math>
Summary
| 2023 ARCADIA at UC Berkeley | Premiere | Y | 2 | 25.00 | 100% | 100% | 50% |
| 2023 ARCADIA at Carleton University | Premiere | Y | 3 | 13.33 | 100% | 0% | 33% |
| 2023 ARCADIA at Claremont Colleges | Premiere | Y | 1 | 20.00 | 100% | 100% | 0% |
| 2023 ARCADIA at Indiana | Premiere | Y | 5 | 18.00 | 80% | 60% | 40% |
| 2023 ARCADIA at RIT | Premiere | Y | 2 | 25.00 | 100% | 100% | 50% |
| 2023 ARCADIA at WUSTL | Premiere | Y | 3 | 3.33 | 33% | 0% | 0% |
| 2023 ARCADIA at Duke | Emory, Duke, Yale | N | 4 | 5.00 | 50% | 0% | 0% |
| 2023 ARCADIA at Emory | Emory, Duke, Yale | N | 4 | 12.50 | 50% | 25% | 50% |
| 2023 ARCADIA at Imperial | Imperial | N | 5 | 18.00 | 80% | 60% | 40% |
| 2023 ARCADIA at Maryland | Maryland, Online | N | 3 | 13.33 | 67% | 33% | 33% |
| 2023 ARCADIA at Ohio State | Ohio State, Texas | N | 3 | 6.67 | 33% | 33% | 0% |
| 2023 ARCADIA Online | Maryland, Online | N | 3 | 16.67 | 67% | 67% | 33% |
| 2023 ARCADIA at Texas | Ohio State, Texas | N | 3 | 13.33 | 67% | 33% | 33% |
Data
| Berkeley C | Berkeley B | 10 | 0 | 10 | 20 |
| Stanford A | Berkeley A | 10 | 10 | 10 | 30 |
| McDouble West-Carleton | Ottawa C | 0 | 0 | 10 | 10 |
| Ottawa A | Ottawa B | 0 | 0 | 10 | 10 |
| Toronto Ray of Sun in the Sky | Waterloo | 0 | 10 | 10 | 20 |
| Claremont | Auxiliary CLU | 10 | 0 | 10 | 20 |
| Illinois A | Indiana | 10 | 10 | 10 | 30 |
| Notre Dame A | Purdue A | 10 | 10 | 10 | 30 |
| Purdue B | Illinois B | 0 | 0 | 10 | 10 |
| Vanderbilt | Notre Dame B | 0 | 0 | 0 | 0 |
| Cornell R | Cornell MATLAB | 10 | 0 | 10 | 20 |
| Chicago A | Chicago B | 10 | 0 | 10 | 20 |
| RIT | Syracuse+Rochester | 10 | 10 | 10 | 30 |
| WUSTL H2O | Squidward Community College | 0 | 0 | 0 | 0 |
| WUSTL XYZ | Missouri A | 0 | 0 | 10 | 10 |
| SIUE | Missouri B | 0 | 0 | 0 | 0 |