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-

Tinku Tara June 4, 2023 Algebra 0 Comments

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

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).

$${n}\:\in\:\mathbb{N}\:{and}\:{p}\:{is}\:{a}\:{prime}\:{number}\:\left({p}\geqslant\mathrm{3}\right). \\ $$$${a}\:{and}\:{b}\:{are}\:{defined}\:{by}:\:{a}=\mathrm{2}^{{n}} \:{and} \\ $$$${b}={a}×{b}.\:\:{S}\left({a}\right)\:{is}\:{the}\:{sum}\:{of}\:{divisors}\: \\ $$$${of}\:{a}\:{and}\:{S}\left({b}\right)\:\:{is}\:{the}\:{sum}\:{of}\:{divisors} \\ $$$${of}\:{b}. \\ $$$$\mathrm{1}.{Determinate}\:{the}\:{set}\:{of}\:{divisors}\:{of} \\ $$$${a}\:{and}\:{the}\:{set}\:{of}\:{divisors}\:{of}\:{b}. \\ $$$$\mathrm{2}.{show}\:{that}\:{S}\left({a}\right)+\mathrm{2}^{{n}+\mathrm{1}} =\mathrm{1}+\mathrm{2}{S}\left({a}\right) \\ $$$${then}\:{calculate}\:{S}\left({a}\right). \\ $$$$\mathrm{3}.\:{write}\:{S}\left({b}\right)\:{in}\:{function}\:{of}\:{S}\left({a}\right)\:{then} \\ $$$${calculate}\:{S}\left({b}\right). \\ $$

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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-

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