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- Title
ON NUMBERS EQUAL TO THE SUM OF TWO SQUARES IN MORE THAN ONE WAY.
- Authors
Ming-Sun Li; Robertson, Kathryn; Osler, Thomas J.; Hassen, Abdul; Simons, Christopher S.; Wright, Marcus
- Abstract
The article shows how a constructive proof was derived from the statement that since r must be the sum of two squares in two different ways, r must be the product of two factors of the same form. The proof demonstrated the use of precalculus mathematics with some number theory. Leonhard Euler said that a number should be written as the product of two factors each of which is the sum of two squares. Many natural numbers cannot be written as the sum of two squares, including 1, 3, 4, 6 and 7. Other numbers cannot be expressed as a product of factors each of which is the sum of two squares. Numbers that can be expressed as the sum of two squares in two or more ways are also considered.
- Subjects
MATHEMATICAL proofs; NATURAL numbers; LEAST squares; NUMBER theory; EULER, Leonhard, 1707-1783; PROOF theory
- Publication
Mathematics & Computer Education, 2009, Vol 43, Issue 2, p102
- ISSN
0730-8639
- Publication type
Article