Date: Thu, 26 Nov 1998 21:00:05 -0400
Pick any odd number, square it, and then divide it by 8. No matter what odd number is chosen and squared and divided by 8, the remainder is one.
Could you please explain this to me or is there a pattern that I am not aware of
Hi again Brenda,
Thus the square of 2k+1 is one more than 4k(k+1). Since k and k+1 are consecutive integers one of them must be even, and hence 2 divides k(k+1). Thus 8 divides 4k(k+1) and hence 4k(k+1)+1 is one more than a multiple of 8. That is dividing 4k(k+1)+1 by 8 leaves a remainder of 1.
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