பித்தகோரசு மும்மை (Tamil Wikipedia)

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arxiv.org

Bernhart, Frank R.; Price, H. Lee (2005). "Heron's formula, Descartes circles, and Pythagorean triangles". arXiv:math/0701624.

For the nonexistence of solutions where a and b are both square, originally proved by Fermat, see Koshy, Thomas (2002), Elementary Number Theory with Applications, Academic Press, p. 545, ISBN 9780124211711. Fpr the other case, in which c is one of the squares, see Stillwell, John (1998), Numbers and Geometry, Undergraduate Texts in Mathematics, Springer, p. 133, ISBN 9780387982892.
Sally, Judith D. (2007), Roots to Research: A Vertical Development of Mathematical Problems, American Mathematical Society, pp. 74–75, ISBN 9780821872673.
This follows immediately from the fact that one of a or b is divisible by four, together with the definition of congruent numbers as the areas of rational-sided right triangles. See e.g. Koblitz, Neal (1993), Introduction to Elliptic Curves and Modular Forms, Graduate Texts in Mathematics, vol. 97, Springer, p. 3, ISBN 9780387979663.

Mitchell, Douglas W. (July 2001), "An Alternative Characterisation of All Primitive Pythagorean Triples", The Mathematical Gazette, 85 (503): 273–5, JSTOR 3622017

Rosenberg, Steven; Spillane, Michael; Wulf, Daniel B. (May 2008), "Heron triangles and moduli spaces", Mathematics Teacher, 101: 656–663