if k is an integer greater than 1 and s is the sum of all the positive divisors of k , is s> k+1 ?
This is rephrased as
Is k not prime?
I didn't understand the above rephrasing.. Please help.
k, a positive integer, will be prime if it has only two divisors - 1 and itself i.e. 1 and k. The sum s of divisors will be 1+k. e.g. prime number 7 has only two divisors 1 and 7. Sum s = 1+7 = 8
If k is not prime, it will definitely have at least one more divisor (in addition to 1 and k itself) and the sum s of divisors will be greater than 1+k. e.g. composite number 9 has 3 divisors: 1, 3, 9. Sum s = 1+3+9 = 13 which is greater than 1+9
The question: Is s > k+1
which translates to 'Is k composite?' or 'Is k not prime'
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