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 set of divisors of b. 2.show that S(a)+2^(n+1) =1+2S(a) then calculate S(a). 3. write S(b) in function of S(a) then calculate S(b).


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

$n \in N a n d p i s a p r i m e n u m b e r (p ⩾ 3) .$ $a a n d b a r e d e f i n e d b y : a = 2^{n} a n d$ $b = a \times b . S (a) i s t h e s u m o f d i v i s o r s$ $o f a a n d S (b) i s t h e s u m o f d i v i s o r s$ $o f b .$ $1 . D e t e r m i n a t e t h e s e t o f d i v i s o r s o f$ $a a n d t h e s e t o f d i v i s o r s o f b .$ $2 . s h o w t h a t S (a) + 2^{n + 1} = 1 + 2 S (a)$ $t h e n c a l c u l a t e S (a) .$ $3 . w r i t e S (b) i n f u n c t i o n o f S (a) t h e n$ $c a l c u l a t e S (b) .$
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