We then offer several questions inviting students to explore extensions of these relationships to other n-note octave divisions. The answers to most questions require only basic properties of modular arithmetic and greatest common divisors. However, some questions ask students to explore additional ...
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For simplicity, Tisa only allows integers to be passed as argu- ments in such remote calls, thus we encode questions using integers: 1 for appoint- ments, 2 for prescriptions, and higher numbers for health-related questions. Contrary to standard black box specifications, internal states of the...
The answers to most questions require only basic properties of modular arithmetic and greatest common divisors. However, some questions ask students to explore additional topics such as Cayley graphs of groups. Thus, the questions can be adapted to fit into a course that appears as early in the...
ARITHMETICRATIONAL numbersWhat is the probability that the smallest part of a random integer partition of N is odd? What is the expected value of the smallest part of a random integer partition of N? It is straightforward to see that the answers to these questions are both 1, to leading ...
Modular arithmetic, in its most elementary form, arithmetic done with a count that resets itself to zero every time a certain whole number N greater than one, known as the modulus (mod), has been reached. Examples are a digital clock in the 24-hour syste