An elementary proof is a proof using methods regarded as basic in the mathematical context under consideration. In number theory, the term commonly refers to a proof that avoids complex analysis, although elementary methods of real analysis may be used (Hoffman 1998, pp. 92-93; Spencer and Graham 2009, p. 18). An elementary proof need not be short or easy.
Elementary Proof
See also
Elementary Methods, Elementary Number Theory, ProofExplore with Wolfram|Alpha
References
Hoffman, P. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. New York: Hyperion, 1998.Spencer, J. and Graham, R. "The Elementary Proof of the Prime Number Theorem." Math. Intelligencer 31, 18-23, 2009. https://doi.org/10.1007/s00283-009-9063-9.Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 22, 1986.Referenced on Wolfram|Alpha
Elementary ProofCite this as:
Weisstein, Eric W. "Elementary Proof." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ElementaryProof.html