On Sums of Seventh Powers

Equal sums of four seventh powers

In this paper, the method used to find the smallest, nontrivial, positive integer solution of a1 + a 7 2 + a 7 3 + a 7 4 = b 7 1 + b 7 2 + b 7 3 + b 7 4 is discussed. The solution is 149 + 123 + 14 + 10 = 146 + 129 + 90 + 15. Factors enabling this discovery are advances in computing power, available workstation memory, and the appropriate choice of optimized algorithms. Introduction Diophantine...

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...

Sums of Seventh Powers in the Ring of Polynomials over the Finite Field with Four Elements

We study representations of polynomials P ∈ F4[T ] as sums P = X7 1 + . . . + X7 s .