Is there any number?

Number Theory Level 3

Find the total number of perfect numbers that are multiples of 96


The answer is 1.

অলক ভট্টাচার্য by অলক ভট্টাচার্য , 66, India

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1 solution

If 2^α-1 be prime, then (2^α-1)2^(α-1) is a perfect number. Thus, (2^2-1)2^(2-1) or 6 is the only perfect number which is a multiple of 3.

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Didnt you ask multiples of 96? As per my knowledge, 6 is not a multiple of 96 ,rather 96 is a multiple of 6.

Further, you should tell 2 a − 1 2^a -1 is only prime when a a is prime. This particular sequence is called Mersenne Primes . Moreover, I prefer you use L a t e x Latex for better presentation of your problems as well as solutions.

A Former Brilliant Member - 2 years, 6 months ago

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