On sums of eighth powers

on direct sums of baer modules

the notion of baer modules was defined recently

On sums which are powers

On powers that are sums of consecutive like powers

1 Background The problem of cubes that are sums of consecutive cubes goes back to Euler ([10] art. 249) who noted the remarkable relation 33 + 43 + 53 = 63. Similar problems were considered by several mathematicians during the nineteenth and early twentieth century as surveyed in Dickson’sHistory of the Theory of Numbers ([7] p. 582–588). These questions are still of interest today. For example...

A Note on Sums of Powers

We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.

On Powers as Sums of Two Cubes

In a paper of Kraus, it is proved that x 3 + y 3 = z p for p 17 has only trivial primitive solutions, provided that p satisses a relatively mild and easily tested condition. In this article we prove that the primitive solutions of x 3 + y 3 = z p with p = 4; 5; 7; 11; 13, correspond to rational points on hyperelliptic curves with Jaco-bians of relatively small rank. Consequently, Chabauty metho...