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Course Queries Syllabus Queries 2 years ago
Posted on 16 Aug 2022, this text provides information on Syllabus Queries related to Course Queries. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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How do I find the solubility of certain non-linear diophantine equations:
For eg.: x4+y4=z4x4+y4=z4 is insoluble in NN, which is easy to prove by infinite descent, but x2+y2=z3x2+y2=z3has infinitely many solutions (which I am apparently stuck with).
The text from where this problem came (Elementary Number Theory, David M. Burton) contains a hint stating to choose x=n(n2−3)x=n(n2−3) and y=3n2−1y=3n2−1 which trivializes the problem. I want to know how to understand the reasoning behind the choice of such substitutions.
Also, as a soft question, is it alright to simultaneously ready An Introduction to the Theory of Numbers by G.H. Hardy along with my present syllabus, or should I focus more on one text?
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