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% |
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