Question

10. Prove that the square ot any positive integer is of the form 4 or 4q1 for some
integer


plz solve ....​

Answer 1

Answer:

let 'a' be any positive integer

b = 4

by Euclid's division lemma,

a = bq + r

a²= (bq + r)²..........1

r = 0,1,2,3

from 1

for r = 0

a²= (4q + 0)²

a²= 16q²

a²= 4(4q²)

= 4q, where q = 4q²

for r = 1

a²= (4q + 1)²

a² = 16q²+ 1 + 8q

a² = 4q + 1, where q = 4q²+2q

Step-by-step explanation:

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