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If one equation be given containing two unknowns, as for example ax + by = c or ax� + by� = c, it is seen that there are an infinite number of roots, for we can give x, say, any value and then determine the corresponding value of y; such an equation is called indeterminate; of the examples chosen the first is a linear and the second a quadratic indeterminate equation.

In general, an indeterminate equation results when the number of unknowns exceeds by unity the number of equations.

A few problems lead to indeterminate equations of the third and fourth degrees, an easy indeterminate equation of the sixth degree being also found.

The solution in integers of the indeterminate equation ax + by = c may be effected by means of continued fractions.

I am x in an indeterminate equation.