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Quadratic Diophantine Equations
\[ \large \color{blue}{x}^2-\color{red}{y}^2=2011\]
How many integral solutions \((\color{blue}{x},\color{red}{y})\) are there for the equation above?
by
Vinay Sipani
\[ \begin{eqnarray} ab+cd&=&38 \\ ac+bd&=&34\\ ad+bc&=&43\\ \end{eqnarray} \]
Let \(a,b,c\) and \(d\) positive integers such that they satisfy the system of equations above. Find \(a+b+c+d\).
by
Paola Ramírez
Find the number of ordered quadruples of positive integers \((x,y,p,q)\) satisfying
\[x^3y-xy^3=pq,\]
and \(p,q\) are prime numbers.
This problem is posed by Daniel C.
by
Calvin Lin
\[\large \frac{1}{x}+\frac{1}{y}=\frac{1}{156}\]
Find the number of ordered pairs of positive integers \((x, y) \) that satisfy the equation above.
by
Vaibhav Prasad
How many ordered tuples of natural numbers \((a,b,c)\) satisfy \[\frac{1}{a}+\frac{1}{ab}+\frac{1}{abc}=1?\]
by
William Lockhart