### Note On The Necessary Condition That Two Linear
Homogeneous Differential Equations Shall
Have Common Integrals

The American Mathematical Monthly, Vol. 10, No. 12 (Dec. 1903), 257-259

Presented to the American Mathematical Society (New York) October 30, 1903

Introduction

Professor Von Escherich in the *Denkschriften der Wiener Akademie*, Vol. 46, and later Heffter in Crelle's *Journal*, Vol. 116, proved that there exists for linear differential homogeneous equations a theory analogous to that of algebraic equations, confining their researches to the analogues to theorems upon the Highest Common Factor and Lowest Common Multiple.

During the past year Dr. Epsteen and Dr. Pierce revived this subject, and in the American Mathematical Monthly, Vol. X, March, 1903, pp. 63-68, Dr. Epsteen gives the necessary condition for one common integral, while Dr. Pierce gives the sufficient condition for k ≥ 1 independent common integrals.

This note gives the necessary condition for two common integrals.