The problems explore divisibility, systems of Diophantine equations
, functional equations, inequalities, trigonometry, chessboard problems, invariants, circles, angles, and lengths of line segments.
Lemma 2 lists all possible trigonometric Diophantine equations
with up to six.
The PSO + GI algorithm was tested on several Diophantine equations
and the results were compared to the standard PSO and SHC.
This contribution uses an algebraic approach based on general solutions of Diophantine equations
Something like 900 years passed by between the time of Pythagoras and the time of Diophantus who worked with what is now called Diophantine equations
Sandor, Geometric theorems, diophantine equations
and arithmetic functions, New Mexico, 2002.
Such equations are called Diophantine equations
in the honour of Diophantus who studied them many centuries ago.
Other themes discussed during that academic year included: the Stolz--Cesaro, the intermediate and the mean value theorems, applications of complex numbers to polynomials, Diophantine equations
, and geometric probability.
Also it is known that the solution of sets of Diophantine equations
is a generator of primes.
In number theory many problems may be posed as diophantine equations
to be solved in integers.
In [1, 2] Quadratic Diophantine equations
with three unknowns have been considered for its parametric integral solutions.
In later years, students who stick with mathematics will learn more about Diophantine equations
in number theory courses.