Question
The Legendre symbol is positive when the top number is one of these values modulo the bottom number. For 10 points each:
[10h] Name these values that appear as solutions to their namesake equations in modular arithmetic. A number a is one of these values modulo p if a is congruent to a perfect square modulo p.
ANSWER: quadratic residues
[10e] This man was the first to prove the law of quadratic reciprocity. He also proved the constructability of the heptadecagon and apocryphally summed the integers from 1 to 100 in minutes as a child.
ANSWER: Johann Carl Friedrich Gauss
[10m] This mathematician is the namesake of a generalization of the Legendre symbol and also names a matrix of partial derivatives used when performing a change of variables.
ANSWER: Carl Gustav Jacob Jacobi
<MH, Other Science>
Summary
| 2023 ILLIAC (Cornell) | 2023-10-21 | Y | 4 | 15.00 | 75% | 75% | 0% |
| 2023 ILLIAC (Mainsite) | 2023-10-21 | Y | 8 | 15.00 | 88% | 50% | 13% |
Data
| Purdue B | Chicago A | 0 | 10 | 10 | 20 |
| Chicago B | Ohio State B | 10 | 10 | 10 | 30 |
| Missouri | Chicago C | 0 | 10 | 0 | 10 |
| Purdue C | Ohio State A | 0 | 10 | 0 | 10 |
| Chicago D | Ohio State C | 0 | 0 | 0 | 0 |
| Michigan B | SIUE A | 0 | 10 | 0 | 10 |
| Purdue A | SIUE B | 0 | 10 | 10 | 20 |
| Michigan A | WUSTL | 0 | 10 | 10 | 20 |