Question

23. How many positive integers between 100 and 999 inclusive a) are divisible by 7? B) are odd? C) have the same three decimal digits? D) are not divisible by 4? E) are divisible by 3 or 4? F ) are not divisible by either 3 or 4? G) are divisible by 3 but not by 4? H) are divisible by 3 and 4?

Answer 1

The following is a list of the known perfect numbers, and the exponents p that can be used to generate them (using the expression 2p−1× (2p − 1)) whenever 2p − 1 is a Mersenne prime. All even perfect numbers are of this form. It is not known whether there are any odd perfect numbers.[1] As of 2018 there are 50 known perfect numbers in total.[2][3][4] The ratio p / digits approaches log(10) / log(4) = 1.6609640474...

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