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Mathematicsresear
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Homework Statement
Prove that for every n greater than or equal to two, there exists a number with exactly n divisors.
Homework Equations
I used induction:
The Attempt at a Solution
Base case: assume n=2 which implies there exists a number with 2 divisors, that is the case for all prime numbers.
Now, let me assume that the statement is true for n=k, now I should show that it is true for n=k+1
which means that for every k+1, there exists an integers with exactly k+1 divisors,
k+1=(q_1...q_kq_k+1)
Now since k+1=(kq_k+1), therefore k divides k+1, and so does k+1 divides k+1.
Is this correct?