Primitive solutions of
x17 + x27 + ... xm7 = y17 + y27 + ... yn7 = z, (1)
for various m,n.

Primitive solutions of (7.2.8):
15 solutions for xmax < 117.

Primitive solutions of (7.3.5):
   order   x            y                      z (factors)
    1.    (96,41,17)   (86,77,77,68,56)      2.5.7.7.43.149.3539.6781 
    2.    (153,43,14)  (140,137,59,42,42)  2.2.3.7.7.7.469321.1016143
   No other solutions for xmax < 187 (i.e., z < 1877)

Primitive solutions of (7.3.7):
20 solutions for xmax < 96.

Primitive solutions of (7.4.5):
8 solutions for xmax < 115.