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How many divisors does an integer with prime factorization have
Let $n$ be an integer with prime factorization $n = p_1^{n_1} p_2^{n_2} ... p_k^{n_k}$ , where the $p_i$ are distinct primes. How many positive divisors does the integer $n$ have?
Here is what I have:
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1
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Prove that, for every natural number, their factorization as primes is unique
I need some feedback on this proof I wrote that:
$$\forall n\in\mathbb{N} \text{ assumed the existence of a factorization of } n \text{ as } n = p_1p_2\cdots p_k, \text{ where } p_i, (1 \leq i \leq k)...
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Application of Unique Factorisation Theorem in Proof
CONTEXT: Proof question made up by uni math lecturer
Suppose you have $x+y=2z$ (where $x$ and $y$ are consecutive odd primes) for some integer $z>1$, and that you need to prove that $x+y$ has at ...
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