Question

2. Prove that if (a, n) = 1, then the set c, c + a, c + 2a, ..., c + (n - 1)a is a complete set of residues (CSR) mod n. Hint: Show that these are all incongruent mod n and apply the pigeonhole principle. b) Corollary: Prove that any n consecutive integers (that is, a, a + 1, a + 2, ..., a + n - 1) form a CSR mod n.

          2. Prove that if (a, n) = 1, then the set c, c + a, c + 2a, ..., c + (n - 1)a is a complete
set of residues (CSR) mod n. Hint: Show that these are all incongruent mod n and
apply the pigeonhole principle.
b) Corollary: Prove that any n consecutive integers (that is, a, a + 1, a + 2, ..., a +
n - 1) form a CSR mod n.

2. Prove that if (a, n) = 1, then the set c, c + a, c + 2a, ..., c + (n - 1)a is a complete
set of residues (CSR) mod n. Hint: Show that these are all incongruent mod n and
apply the pigeonhole principle.
b) Corollary: Prove that any n consecutive integers (that is, a, a + 1, a + 2, ..., a +
n - 1) form a CSR mod n.

Added by Christine M.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Jim Long

Step 1

.., c + (n-1)a are incongruent mod n. Assume that there exist two numbers in the set, say c + ka and c + la, where k ≠ l, that are congruent mod n. This means that (c + ka) - (c + la) is divisible by n. Simplifying, we get ka - la = (k - l)a is divisible by n. Show more…

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Prove that if a^n = 1, then the set c, c + ac + 2a, ..., c + (n-1)a is a complete set of residues (CSR) mod n. Hint: Show that these are all incongruent mod n and apply the pigeonhole principle. Corollary: Prove that any n consecutive integers (that is, a, a+1, a+2, ..., a+n-1) form a CSR mod n.