Question

show that the square of any integer is either of the form 4q or 4q +1 for some integer m​

Answer 1

Step-by-step explanation:

Let positive integer a = 4m + r , By division algorithm we know here 0 ≤ r < 4 , So

When r = 0

a = 4m

Squaring both side , we get

a2 = ( 4m )2

a2 = 4 ( 4m2)

a2 = 4 q , where q = 4m2

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