On Sums of Seventh Powers Original Research Article

By means of an identity it is proved that every integer is the sum or difference of 12 integral seventh powers and every rational member is the sum or difference of 8 seventh powers of rational numbers. A parametric solution in positive integers of the diophantine equation ∑4i=1 x7i=∑5i=1 y7i is obtained and it is also shown how solutions in positive integers of the equation ∑mi=1 x7i=∑ni=1 y7i may be obtained whenever mgreater-or-equal, slanted4 and ngreater-or-equal, slanted5.