How many prime numbers p, are there such that 6p-27 is the cube of the positive integer?

How many prime numbers p, are there such that 6p-27 is the cube of the positive integer?

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2 thoughts on “How many prime numbers p, are there such that 6p-27 is the cube of the positive integer?”

  1. Step-by-step explanation:

    (1) p/4 is a prime number –> p = 4*(prime number) –> p can be 4*2=8, 4*3=12, 4*5=20, 4*7=28, … Not sufficient.

    (2) p is divisible by 3 –> p can be 3, 6, 9, 12, 15, … Not sufficient.

    (1)+(2) From (1) we have that p = 4*(prime number) and from (2) that p is a multiple of 3. Now, for p = 4*(prime number) to be a multiple of 3 (prime number) must be 3, hence p = 4*(prime number) = 4*3 = 12.

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