Question

prove that square of any
integer
remainder either o or 1 when
the divided
by
4.​

Answer 1

Answer:

Square of any integer remainder either o or 1 when the divided by4.​

Step-by-step explanation:

Any integer can be in the form of 2n or 2n-1

Case I let x=2n

x²=4n²

Now 4n² mod 4 =0..............(1)

Case II x=2n-1

x²=(2n-1)²

=4n²-4n+1

=4n(n-1)+1

=4nm+1 ( m=n-1 is an integer)

=4p+1  ( p=mn is an integer

So 4p+1 mod 4=1...................(2)

From 1) and 2)

Square of any integer remainder either o or 1 when the divided by4.​