Tagged Questions
4
votes
2answers
60 views
Foundation on Diophantine Analysis and Number Theory
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
...
13
votes
2answers
230 views
How did Letac solve $x_1^k + x_2^k + \dots +x_9^k = 0$ for $k = 1, 3, 5, 7$ in 1942?
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,
$$1 + 5^k + (3+2y)^k + (3-2y)^k + (-3+3y)^k + ...
14
votes
1answer
446 views
How to compute rational or integer points on elliptic curves
This is an attempt to get someone to write a canonical answer, as discussed in this meta thread. We often have people come to us asking for solutions to a diophantine equation which, after some clever ...
1
vote
1answer
91 views
Diophantine Equation $x^n+y^n=z^n$
Problem
Using simple mathematical operators (+,- ,> etc.) can it be shown that (assuming $ x<y$) Fermat’s theorem is always true when $$ n\ge x$$
Request I am sure this approach has been ...
10
votes
1answer
173 views
Diophantine equation $x^y-y^x=11$
How can one find all integer solutions to $x^y-y^x=k$, for a given k?
Example case $x^y-y^x=11$
5
votes
4answers
244 views
Is there a catalogue of solved Diophantine equations?
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 ...
1
vote
0answers
147 views
Quadratic fields and solving Diophantine equations
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 ...
3
votes
0answers
221 views
Counting Solutions of Diophantine Inequalities
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
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