Show that square of any positive is of the form 4m or 4m+1 , when m is an integer.
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Show that square of any positive is of the form 4m or 4m+1 , when m is an integer.
Show that square of any positive is of the form 4m or 4m+1 , when m is an integer.
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Answer:
Let "A" be any positive integer and "b=4".
Apply edl for this.
Possible remainders are 0,1,2 or 3.
Therefore A can be in the form of
4q+1,4q+2,4q+3
Now, (4q)2=4(4)*Q2
=16q2
=4(4q2)
=4m
Again,(4q+1)2=(4q)2+1+8q
=16q2+8q+1
=4(4q2+2q)+1
=4m+1
Therefore square of all positive integers is of the form 4m,4m+1.
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