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This is a plea for where I can find info' on a topic. I have solved the question but need to know if other (general) methods exist and also to learn and try out more difficult problems along similar lines.

How solve [$20x-3$]=[$15x+27$]

[$x$] = integer part of $x$

I have the full solution which is spread out over five intervals. But I am keen to know if there is a general body of work on this topic and similar equations like

[$ax+b$]=[$cx+d$]

and variations of this with simultaneous equations and quadratics etc. Thanks in advance.

Quadratic Reciprocity
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    I'd be surprised if anyone has written a paper about these topics. I think the general idea is to use the definition of $[x]$ and to rely on general algebraic skills to get to an answer. – Gerry Myerson Dec 02 '20 at 22:17
  • I hope you're wrong Gerry but my efforts at Googling and flicking through dozens of textbooks has turned up nothing amounting to a 'body of work' on this topic. Nonetheless I will continue my own little efforts as it is such good fun! – Quadratic Reciprocity Dec 02 '20 at 22:51

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