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Sagot :
The statement that "σ(n) < 2n holds true for all n of the form n = p²" has been proved.
Let p be any prime number, and let σ(n) be the sum of all positive divisors of the integer n.
As p is a prime number, and 2 is the smallest prime number, so, p[tex]\geq[/tex]2
So, the positive divisors of the integer n are: 1,p,p².
As σ(n) represents the sum of all positive divisors of the integer n.
σ(n)=1+p+p²
In order to prove that σ(n) < 2n,for all n of the form n = p².
1+p+p²<2p²
p²-p-1>0
It is know that, p[tex]\geq[/tex]2.
So, p²-p-1[tex]\geq[/tex]1
Thus, σ(n) < 2n holds true for all n of the form n = p².
Learn more about prime numbers here:
https://brainly.com/question/145452
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