In an earlier paper [11] we have discussed the diophantine equation
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0025579300010068/resource/name/S0025579300010068_eqn1.gif?pub-status=live)
and the more general equation
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0025579300010068/resource/name/S0025579300010068_eqn2.gif?pub-status=live)
when l is an odd prime > 3, c a natural number (or more generally a rational number) satisfying several conditions, n also a natural number and x, y, z, non-zero rational integers. Other investigators have obtained quite a number of results concerning particularly the case n = 1. Obviously, without an essential restriction, we may assume that the natural number c contains no divisor a1n (since such a divisor can be absorbed in the power of z) and furthermore that x, y, z in (1) are relatively prime in pairs.