I want to read particularly about diophantine Analysis and Elementary Number Theory from a novice level. The books which I found on net: A Guide to Elementary Number Theory by Underwood Dudley ...
It's quite easy to find integer solutions to, $$x_0^k + x_1^k + \dots +x_9^k = 0$$ for $k = 1, 3, 5, 7$. One I found is, if $x^2-10y^2 = 9$, then, $$1 + 5^k + (3+2y)^k + (3-2y)^k + (-3+3y)^k + ...
This is an attempt to get someone to write a canonical answer, as discussed in this meta thread. We often have people come to us asking for solutions to a diophantine equation which, after some clever ...
Problem Using simple mathematical operators (+,- ,> etc.) can it be shown that (assuming $ x<y$) Fermat’s theorem is always true when $$ n\ge x$$ Request I am sure this approach has been ...
How can one find all integer solutions to $x^y-y^x=k$, for a given k? Example case $x^y-y^x=11$
Is there a book, website or something else aiming to catalogue all or many of the Diophantine equations that have already been solved? I have two tiny books by Sierpiński in which he gives some of ...
I would like to learn to solve Diophantine equations and I think my next step would be quadratic fields or number fields. What are kind of methods there are to use those on solving equations? And what ...
I understand that Diophantine Analysis is an enormous field! Without first determining the solution set, suppose I'd like to calculate the number of non-negative integer solutions $(x,y,z)$ of ...