EQUAL SUMS OF SEVENTH POWERS

AJAI CHOUDHRY

Abstract:

Until now only three numerical solutions of the diophantine equation $x^7_1+x^7_2+x^7_3+x^7_4=y^7_1+y^7_2+y^7_3+y^7_4$ are known. This paper provides three numerical solutions in positive integers of the hitherto unsolved system of simultaneous diophantine equations $x^k_1+x^k_2+x^k_3+x^k_4=y^k_1+y^k_2+y^k_3+y^k_4$, $k=1,3$ and 7.