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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, p2
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, p2.
So, p²-p-11
Thus, σ(n) < 2n holds true for all n of the form n = p².
Learn more about prime numbers here:
brainly.com/question/145452
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If Mel drove 432 miles and drove an average of 72 miles per hour, the Trip would have taken 6 hours answer B
Explanation:
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In the north bank there are four boxes for clients to withdraw money at the beginning of the morning, the four boxes have different amounts of coins and bills. Calculate how much each client will receive according to the box they go to in case they cannot extract the total, explain why?
The lake would most likely form in the number 20 because all lakes stream in some salty water hope this made sense!