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Conversations on greatest common divisor
Today I am going
to share with you
an interesting
conversation
between me and
my cousin Apoorvi,
who is a curious
student of class 9.
This conversation
began after she
saw me teaching
Greatest Common
Divisor to Priyanka.
Priyanka lives in
my neighborhood
and she is a student
of class four.
Sometimes she visits
my home for help in
mathematics. One
day after helping
Priyanka with her
homework, I started
talking to Apoorvi
The Distribution of the Greatest Common Divisor of Elements in Quadratic Integer Rings
For a pair of quadratic integers n and m chosen randomly, uniformly, and independently from the set of quadratic integers of norm x or less, we calculate the probability that the greatest common divisor of (n,m) is k. We also calculate the expected norm of the greatest common divisor (n,m) as x tends to infinity, with explicit error terms. We determine the probability and expected norm of the greatest common divisor for quadratic integer rings that are unique factorization domains. We also outline a method to determine the probability and expected norm of the greatest common divisor of elements in quadratic integer rings that are not unique factorization domains
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