N2 leaves a remainder of 1 when divided by 24 What are the possible remainders we can get if we divi...........

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N² leaves a remainder of 1 when divided by 24. What are the possible remainders we can get if we divide N by 12?

1, 5, 7 and 11

1 and 5

5, 9, and 11

1 and 11

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Explanation:

N is an odd number. So, the remainder when we divide N by 24 has to be odd.
If the remainder when we divide N by 24 = 1, then N² also has a remainder of 1.
we can also see that if the remainder when we divide N by 24 is -1, then N² a remainder of 1.
When remainder when we divide N by 24 is ±3, then N² has a remainder of 9.
When remainder when we divide N by 24 is ±5, then N² has a remainder of 1.
When remainder when we divide N by 24 is ±7, then N² has a remainder of 1.
When remainder when we divide N by 24 is ±9, then N² has a remainder of 9.
When remainder when we divide N by 24 is ±11, then N² has a remainder of 1.
So, the remainder when we divide N by 24 could be ±1, ±5, ±7 or ±11.
Or, the possible remainders when we divide N by 24 are 1, 5, 7, 11, 13, 17, 19, 23.
Or, the possible remainders when we divide N by 12 are 1, 5, 7, 11.