Q1 of 57 Page 23

Show that the square of an odd positive integer is of the form 8q + 1, where q is a positive integer.

Let a be any positive integer.

Then a = 8m + 1 where m is some integer


a = 8m + 1


⟹ a2 = (8m + 1)2


= 64m2 + 16m + 1


= 8q + 1


Where q = 8m2 + 2m


Hence square of an odd integer is of the form 8q + 1 where q is a positive integer.


More from this chapter

All 57 →
2

By Euclid Division Lemma show that the cube of any positive integral number is of the form 9q or 9q + 1 or 9q + 8, where q is an integral number.

 3

Show that any positive odd integral number can be expressed as 6q + 1 or 6q + 3 or 6q + 5 where q is a positive integer.

 4

Find the HCF (Highest Common Factor) of the following pairs of number by Euclid Division Algorithm:

210, 55


 4

Find the HCF (Highest Common Factor) of the following pairs of number by Euclid Division Algorithm:

420, 130