Question

If Y = {x | x is a positive factor of the number 2^{p – 1} (2^p – 1), where 2^p – 1 is a prime number}.Write Y in the roaster form.

Answer 1

Y = {x | x is a positive factor of the number 2^{p – 1} (2^p – 1), where 2^p – 1 is a prime number}.

Roster form of given set.

Only possible positive factors of a prime number p are 1 and p itself.

Possible factors of 2^p – 1 (2^p – 1) are all possible factors of 2^p – 1 and 2^p – 1 individually.

Possible factors of 2^p – 1 are 2⁰, 2¹ ... 2^p – 1 ate 1 and 2^p – 1  ....[∵ 2^p – 1 is prime number]

Therefore, x = 1, 21 ... 2^{p – 1},. 2^p – 1

Hence, Y = {1, 2¹ ... 2^{p – 1}, 2^p – 1}