BIQUADRATIC DIOPHANTINE EQUATIONS WITH INTEGER SOLUTIONS: BIQUADRATIC DIOPHANTINE EQUATIONS

involves solving polynomial equations in integers. It is well known that

a Diophantine equation is an equation with integer coefficient and

multiple variables ( 2) having integer solutions. There is no universal

method available to know whether a Diophantine equation has a

solutions or finding all solutions, if it exists. Proving that even simple

Diophantine equations have no solutions may require very

sophisticated methods and in such cases, a lot of deep and beautiful

mathematics get generated as a result. It is worth to observe that

Diophatine equations are rich in variety. A collection of special

Problems on biquadratic equations in 3,4,5 & 6 variables has been

treated in sections A to D respectively. Different sets of integer solutions

to each of the biquadratic diophatine equations are illustrated.