Generalized Fermat Equations and the Conjecture of Erdős

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发表日期：

2025年

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Saradha Natarajan

摘要

In 1637, the Frenchman Pierre de Fermat stated that the equation \( x^\ell +y^\ell =z^\ell \) does not have any solution in non-zero integers for any integer \(\ell >2.\) When \(\ell =2,\) we get Pythagorean equation and it is well known that there are infinitely many integral solutions.

In 1637, the Frenchman Pierre de Fermat stated that the equation \( x^\ell +y^\ell =z^\ell \) does not have any solution in non-zero integers for any integer \(\ell &gt;2.\) When \(\ell =2,\) we get Pythagorean equation and it is well known that there are infinitely many integral solutions.

Generalized Fermat Equations and the Conjecture of Erdős

摘要

In 1637, the Frenchman Pierre de Fermat stated that the equation \( x^\ell +y^\ell =z^\ell \) does not have any solution in non-zero integers for any integer \(\ell >2.\) When \(\ell =2,\) we get Pythagorean equation and it is well known that there are infinitely many integral solutions.