110 MAJOR P. A. MxcMAHON ON THE COMPOSITIONS OF NUMBERS. 



SECTION 7. 



Generalisation of the Multiplication Theorem. 

 Art. 70. I will establish the result 



where the summation is for all solutions of the diophantine equations 



\ + ri+... = la, 



=P, 



For consider 



N W 



the summation being for all solutions of the diophantine equations 



r,+r 2 = r, 



Moreover, 



and, by like reasoning, the theorem as enunciated follows. 



