Known substantive errata in 2019 or 2020 edition: In subsubsection 3.4.2.1 on Pythagorean triples, z=m+n and x=n-m, not the other way around. Thanks to Mike Spivey for noticing this. In Fact 15.3.5 on the Bachet equation, there are a couple of places with x^2 or linear factors in x which should actually be y^2 and in y. Thanks to user Jeikai Zheng for pointing this out. In Example 17.2.5 we should have 3^5, not 2^5, and in the following Fact the exponent should be r_{a,e}, not just r_e. Thanks to anonymous user "niwox" for pointing this out. In Example 20.4.2 there should be two additional "+1" in the second part. Thanks to Pieter Geerkens for pointing this out. After Definition 22.2.6, in the last bullet point, there should be p# not q#. Thanks to Pieter Geerkens for pointing this out.