Question

Show that square of any odd integer is of the form 4q+1for some integer q.​

Answer 1

Answer:

Let a be any odd integer and b = 4. Then, by Euclid's algorithm, a = 4m + r for some integer m ≥ 0 and r = 0,1,2,3 because 0 ≤ r < 4. ... = 4q + 1, where q is some integer. Hence, The square of any odd integer is of the form 4q + 1, for some integer q

Step-by-step explanation:

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Answer 2

Answer:

We know that any positive odd integer of the form 2m +1, 2m +3

let a be an odd integer

then

a = 2m + 1

on squaring both sides we get

a² = (2m +1)²

a² = 4m²+4m+1

a²= 4(m²+m) + 1.

a² = 4q + 1.

( where (m²+m) = q)

Hence proved