Q5 of 53 Page 1

Prove that the square of any positive integer of the form 5q + 1 is of the same form.

Given: Integer N > 0


To prove: N2 = 5q + 1


Proof:


Let N = 5p + 1. Then,


According to the condition:


N2 = 25p2 + 10p + 1


⇒ 5(5p2 + 2p) + 1


⇒ 5q+1


Where q = 5p2 + 2p


Therefore, N2 is of the form 5q + 1.


More from this chapter

All 53 →
3

Is 43.123456789 is a rational number of the form or not? If yes, write the factors of q.

 4

Express 5005 as product of its prime factors.

 6

Use Euclid’s division algorithm to find the HCF of 196 and 38220.

 7

Prove that if a positive integer is of the form 6q + 5, then it is of the form 3q + 2 for some integer q, but not conversely.