A NOTE ON THE DIOPHANTINE EQUATION P(z) = n!+m!

作者：Gawron Maciej^*

来源：Colloquium Mathematicum, 2013, 131(1): 53-58.

DOI：10.4064/cm131-1-5

• Brocard-Ramanujan type equation
• ABC Conjecture
• Diophantine equation

We consider the Brocard-Ramanujan type Diophantine equation P(z) = n! + m!, where P is a polynomial with rational coefficients. We show that the ABC Conjecture implies that this equation has only finitely many integer solutions when d %26gt;= 2 and P(z) = a(d)z(d) + a(d-3)z(d-3) + ... + a(1)x + a(0).

• 出版日期2013