Practice Helping Lemma - 11.2.4 | 11. Uniqueness Proof of the CRT | Discrete Mathematics - Vol 3
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Helping Lemma

11.2.4 - Helping Lemma

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does it mean for a number 'a' to divide 'b'?

💡 Hint: Think about the division operation.

Question 2 Easy

State Euclid's Lemma in your own words.

💡 Hint: Relate it to an example you’ve seen.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does Euclid’s Lemma state?

p divides the product implies p divides none of them
p divides the product implies p divides at least one of them
p is always greater than one

💡 Hint: Think about how prime factors interact with products.

Question 2

True or False: The Helping Lemma assures the existence of unique solutions in CRT.

True
False

💡 Hint: Remember the implications of congruences and moduli.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the congruences x ≡ 3 mod 4, x ≡ 4 mod 5, and x ≡ 2 mod 6, find all possible values of x.

💡 Hint: You must consider each modulus and their pairwise relations.

Challenge 2 Hard

Demonstrate why the Chinese Remainder Theorem cannot work if the moduli are not pairwise coprime, with a specific example.

💡 Hint: Think about divisibility and overlap in factors.

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