A theorem with constructive and non-constructive proofs

TL;DR

This paper presents a straightforward example of a theorem that admits both constructive and non-constructive proofs, illustrating differences in proof methods within mathematics.

Contribution

It provides a simple, explicit example of a theorem with both constructive and non-constructive proofs, highlighting proof technique distinctions.

Findings

The equation c^2 x^2 - (c^2 + c)x + c = 0 has solutions.

The theorem can be proved constructively and non-constructively.

The example clarifies differences between proof methods.

Abstract

We present a very simple example of a theorem with constructive and non-constructive proofs: the equation c^2 x^2 - (c^2 + c)x + c = 0 has a solution.