Question

that the square of any positive integer is of the form 4m or 4m+1 for some integer m
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Answer 1

Answer:

a=bq+r

r=0,1

b=2

when r=0

a^2 = 4q^2

a^2 = 4m , where m = q^2

when r=1

a^2 = 4q^2 + 4q + 1

a^2 = 4 ( q^2 + q ) + 1

a^2 = 4m + 1 , where m = q^2 + q

so , square of any positive integer is of the form 4m or 4m + 1