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anemone
Gold Member
MHB
POTW Director
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Show that $3^{2008}+4^{2009}$ can be written as a product of two positive integers each of which is larger than $2009^{182}$.
Yes, it can be written as a product of two positive integers.
The factors of $3^{2008}+4^{2009}$ are $3^{2008}$ and $4^{2009}$.
No, $3^{2008}+4^{2009}$ is not a prime number as it can be factored into two positive integers.
No, $3^{2008}+4^{2009}$ cannot be written as a power of a single number as it is the sum of two distinct powers.
Yes, the factors of $3^{n}+4^{n}$ can be expressed as $(3^{k}+4^{k})(3^{n-k}-4^{n-k})$ where $k$ is any integer from $0$ to $n$.