The greatest achievement was at first, and for a time, but a dream. – **Napoleon Hill**

# Part - 3 Lecture - 2 Chapter 1 Real Numbers

Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.

00:03:32 Question 4. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

00:20:02 Question 6. Show that the square of any positive integer is either of the form 4q or 4q + 1 for some integer q.

00:28:02 Question 8. Prove that the square of any positive integer is of the form 5q, 5q + 1, 5q + 4 for some integer, q.

00:45:42 Question 5. Show that square of any odd integer is of the form 4m + 1, for some integer m.

00:52:32 Question 7. Show that the square of an odd positive integer is of the form 8m + 1, for some whole number m.