what are the possible remainders when a perfect square is divided by 11?
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All numbers can be expressed in the form
(11p+r), r is the remainder after division by 11
r is in the range 0, 1, 2, 3,4,5,6,7,8,
(11p+0)(11p+0)=121p^2, remainder is 0
(11p+1)(11p+1)=121p^2+11p+11p+1=121p^2+22p+1, remainder is 1
(11p+2)(11p+2)=121p^2+22p+22p+4=121p^2+44p+4, remainder is 4
(11p+3)(11p+3) = 121p^2+33p+33p+9=121p^2+66p+9, remainder is 9
(0, 1, 4, 9) are the possible remainders
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