Express 2015 as a sum of distinct powers of 2. Is 83 prime? Find the smallest prime larger than 800. A positive integer, n, has property P if n is equal to the sum of its positive divisors (not...

Express 2015 as a sum of distinct powers of 2.

Is 83 prime?

Find the smallest prime larger than 800.

A positive integer, n, has property P if n is equal to the sum of its positive divisors (not including itself). Demonstrate that the following numbers have property P:

(a) 6

(b) 28

(c) 496

(d) 8128

A positive integer, n, has property Q if n is less than the sum of its positive divisors (not including itself). Demonstrate that the following numbers have property Q:

(a) 12

(b) 20

(c) 30

(d) 36