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# Solve the following problems about equivalence mod n.a. Use the definition of equivalence mod n to explain why each statement is true.i. 23 $\equiv$ 8 mod 5ii. 76 $\equiv$ 4 mod 9iii. -3 $\equiv$ 24 mod 27b. Find four integers that are equivalent to 2 mod 27. At least one of the numbers should be a negative integer.c. Working with others, brainstorm a possible equivalent, yet different, definition or description of "equivalent mod n. "

Solution

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a.) i

$23\equiv8$ in mod $5$ because $23\div5$ and $8\div5$ both have a remainder of $3$.

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