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The aim of this expository article is twofold. The first is to introduceseveral polynomials of one variable as well as two variables defined on thepositive integers with values as congruent numbers. The second is to presentconnections between Pythagorean triples and the Pell equation $x^2-dy^2=1$ plusits analogous counterpart $x^2-dy^2=-1$ which give rise to congruent numbers nwith arbitrarily many prime factors.

Congruent Numbers Via the Pell Equation and its Analogous Counterpart