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प्रश्न
The remainder when the square of any prime number greater than 3 is divided by 6, is
विकल्प
1
3
2
4
उत्तर
Any prime number greater than 3 is of the form `6k +- 1`, where k is a natural number.
Thus,
`( 6k +- 1)^2= 36k^2+-12k+1`
`= 6k (6k+-2)+1`
When, `6k(6k+-2)+1` is divided by 6, we get, `k(6k+-2)`and remainder as 1.
Hence, the correct choice is (a).
Notes
[Hint: Any prime number greater than 3 is of the from 6k ± 1, where k is a natural number and (6k ± 1)2 = 36k2 ± 12k + 1 = 6k(6k ± 2) + 1]
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