1.

Show that the square of an odd integer is of the form 4q + 1 from some integer q​

Answer»

Answer:

Step-by-step explanation:

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

LET a be any 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)

proved.....

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