Solutions manual for NTB - 2.2 Definitions and basic properties of congruences

Exercise 2.3. Let with . Show that iff .

Proof

(q.e.d)

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Exercise 2.4. Let with and . Also, let . Show that:

.

Proof

(q.e.d)

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Exercise 2.5. Let with , , and . Show that if , then .

Proof

(q.e.d)

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Exercise 2.6. Let with , , and . Show that if and , then .

Proof

(q.e.d)

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Exercise 2.7. Let with and . Show that .

Proof

(q.e.d)

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Exercise 2.10. Show that the equation has no solutions .

Proof

(q.e.d)

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