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Number Theory

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Moderate

Fermat Number: Finding GCD and LCM

NUMTH-RVPLOZ

Fermat number is a positive integer of the form:

$$ F_n = 2^{2^n}+1 $$

...for a nonnegative integer $n$.

What is the least common multiple of $F_m$ and $F_n$? Select ONE answer which is always true.

A

$F_n$.

B

$F_{mn}$.

C

$F_{[m,n]}$ where $[m,n]$ is the least common multiple of $m$ and $n$.

D

$\begin{cases} F_mF_n &\mbox{ if $m$ and $n$ are distinct, }\\\ F_m &\mbox{ otherwise. }\end{cases} $

E

$\begin{cases} F_mF_n &\mbox{ if $m$ nad $n$ are relatively prime, }\\\ 1 &\mbox{ otherwise. }\end{cases}$