which enumerates the partitions of a number 283 



From the first relation 



I €1220 = ftse + «48 + a46 + a25 + «21 



=0+1+0+0+0 

 «216 = «54 + «47 + «45 + «24 + «20 

 =1+0+0+1+1 



= 1. 



Thence 



f^ieOO = ^^250 + ^243 + f''241 + ^^220 + CI21S + Cf]81 + CI175 + flfi26 + Cf]18 + Q'ss + f'45 



=1+0+0+1+1+1+0+0+1+0+0 



= 1, 



establishing, in about five minutes work, that j^iooo is an uneven 

 number. 



