# Difference between revisions of "Real Numbers"

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Session # 9 [https://youtu.be/K1-b2hat-ME/ Euclid's Division Lemma - Applications] | Session # 9 [https://youtu.be/K1-b2hat-ME/ Euclid's Division Lemma - Applications] | ||

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+ | ==Problems== | ||

+ | [https://youtu.be/KR4BRId5E7I/ Problem Solving Session # 1] Show that n^2-1 is divisible by 8 if n is an odd positive integer. | ||

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+ | [https://youtu.be/nvMBua1yNoE/ Problem Solving Session # 2] Show that the square of any positive integer is of the form of 3m or 3m+1 for some integer m. | ||

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+ | [https://youtu.be/Rk5-XKjq1-U/ Problem Solving Session # 3]Prove that one of every three consecutive positive integers is divisible by 3 | ||

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Session # 10 [https://youtu.be/VF4NtFu4Qgw/ Euclid's Division Algorithm] | Session # 10 [https://youtu.be/VF4NtFu4Qgw/ Euclid's Division Algorithm] |

## Revision as of 18:42, 16 March 2019

Concepts Lectures on Real Numbers and Divisibility

# Concept Lectures

Session # 1 What are Real Numbers?

Session # 2 What is meant by divisibility?

Session # 3 Properties of divisibility : Part 1

Session # 4 Properties of divisibility : Part 2

Session # 5 Euclid's Division Lemma : Part 1

Session # 6 Euclid's Division Lemma : Part 2

Session # 7 Euclid's Division Lemma : Part 3

Session # 8 Proof of the Euclid's Division Lemma

Session # 9 Euclid's Division Lemma - Applications

## Problems

Problem Solving Session # 1 Show that n^2-1 is divisible by 8 if n is an odd positive integer.

Problem Solving Session # 2 Show that the square of any positive integer is of the form of 3m or 3m+1 for some integer m.

Problem Solving Session # 3Prove that one of every three consecutive positive integers is divisible by 3

Session # 10 Euclid's Division Algorithm

Session # 11 Euclid's Division Algorithm: What is GCD?

Session # 12 Euclid's Division Algorithm: What are co-prime numbers?

Session # 13 Euclid's Division Algorithm: Finding GCD of Two Positive Integers

Session # 14 Euclid's Division Algorithm: Theorem 1 and its proof

Session # 15 Expressing GCD of Two Positive Integers as a Linear Combination

Session # 16 Fundamental Theorem of Arithmetic

# Problem Solving Sessions

Problem Solving Session # 1 Show that n^2-1 is divisible by 8 if n is an odd positive integer.

Problem Solving Session # 2 Show that the square of any positive integer is of the form of 3m or 3m+1 for some integer m.

Problem Solving Session # 3Prove that one of every three consecutive positive integers is divisible by 3