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3
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If a prime and its square both divide a number n, prove that $n=a^2 b^3$
Lets call a number $n$ a fortified number if $n>0$ and for every prime number $p$, if $p|n$ then $p^2|n$. Given a fortified number, prove that there exists $a,b$ such that $n=a^2b^3$.
I know that ...
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6
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What is sum of totatives of n(natural numbers $ \lt n$ coprime to $n$ )?
Same question as in title:
What is sum of natural numbers that are coprime to $n$ and are $ \lt n$ ?
I know how to count number of them using Euler's function, but how to calculate sum?
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0
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Prime Factorizations that divide each other
Let n have prime factorization n = p^s1 · p^s2 · · · p^sk
and let m have prime factorization m = q^t1 · q^t2 · · · q^tl
If n|m, what must be true about the corresponding lists of primes and the ...
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