If I have this GCD equation: $$89=16\cdot5+9\\ 16=9\cdot1+7\\ 9=7\cdot1+2\\ 7=2\cdot3+1\\ 2=1\cdot2+0$$
Then my continued fraction will be:
$[5: 1, 1, 3, 2]$
But if I will have this GCD equation:
$$300=99\cdot3+3\\ 99=3\cdot33+0$$
Then my continued fraction will be:
$[3: 33]$
Is it possible for a continued fraction have only $2$ numbers in total (like the one stated above)?
As mentioned in the comments, it is perfectly fine for a continued fraction to contain only two numbers.
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