Question
In 2005, the only surviving portrait of this mathematician was discovered to actually be of an obscure politician who shares his last name. For 10 points each:
[10e] Name this French mathematician whose namesake symbol is equivalent to the Jacobi symbol if p is an odd prime. His namesake transform converts a function of one set of variables to a function of a conjugate set of variables, producing the Hamiltonian from the Lagrangian.
ANSWER: Adrien-Marie Legendre [accept Legendre symbol or Legendre transform]
[10m] The Legendre symbol returns positive 1 if a is one of these values modulo p, meaning that there exists a perfect square x such that x is congruent to a mod p.
ANSWER: quadratic residue [prompt on residues]
[10h] One can determine if an integer is a quadratic residue using Euler’s criterion, which states that the Legendre symbol of a over p is congruent to this function of a and p, mod p.
ANSWER: a raised to the power p minus 1 over 2 [accept answers that use one-half p minus one-half]
<RR>
Summary
| 2023 BHSU @ Berkeley | 03/18/2023 | Y | 3 | 16.67 | 100% | 67% | 0% |
| 2023 BHSU @ Maryland | 03/11/2023 | Y | 3 | 10.00 | 67% | 33% | 0% |
| 2023 BHSU @ Northwestern | 02/25/2023 | Y | 6 | 15.00 | 83% | 50% | 17% |
| 2023 BHSU Online | 04/15/2023 | Y | 4 | 15.00 | 100% | 25% | 25% |
| 2023 BHSU @ Sheffield | 04/15/2023 | Y | 2 | 20.00 | 100% | 100% | 0% |
Data
| Berkeley B | Berkeley A | 10 | 10 | 0 | 20 |
| It's Joever | Stanford B | 10 | 0 | 0 | 10 |
| Stanford A | [Insert Lawyer Joke Here] | 10 | 10 | 0 | 20 |