n-N-and-p-is-a-prime-number-p-3-a-and-b-are-defined-by-a-2-n-and-b-a-b-S-a-is-the-sum-of-divisors-of-a-and-S-b-is-the-sum-of-divisors-of-b-1-Determinate-the-set-of-divisors-of-a-and-the-

Question Number 124107 by mathocean1 last updated on 30/Nov/20

n \in N a n d p i s a p r i m e n u m b e r (p ⩾ 3) .

a a n d b a r e d e f i n e d b y : a = 2^{n} a n d

b = a \times b . S (a) i s t h e s u m o f d i v i s o r s

o f a a n d S (b) i s t h e s u m o f d i v i s o r s

o f b .

1 . D e t e r m i n a t e t h e s e t o f d i v i s o r s o f

a a n d t h e s e t o f d i v i s o r s o f b .

2 . s h o w t h a t S (a) + 2^{n + 1} = 1 + 2 S (a)

t h e n c a l c u l a t e S (a) .

3 . w r i t e S (b) i n f u n c t i o n o f S (a) t h e n

c a l c u l a t e S (b) .