- #1

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- TL;DR Summary
- Given are non-negative integer squared variables according to ##C=x^2+y^2+z^2##. I am trying to deduce the absolute difference between a certain value of ##C=x^2+y^2+z^2## and the very next smallest increase in ##C## possible so I can (dis)prove the following

- Whether small absolute differences occur less frequently at higher values of ##C##

- Whether larger absolute differences start appearing at higher values of ##C##

Given are non-negative integer variables ##x##, ##y## and ##z##. I am trying to deduce the absolute difference between a certain value of ##C=x^2+y^2+z^2## and the very next smallest increase in ##C## possible.

I'd like to do this so I can (dis)prove the following:

However, I'm not sure how to do this and/or whether there is another simpler approach to this problem.

I'd like to do this so I can (dis)prove the following:

- Whether small absolute differences occur less frequently at higher values of ##C##
- Whether larger absolute differences start appearing at higher values of ##C##

However, I'm not sure how to do this and/or whether there is another simpler approach to this problem.