In this paper we prove that every integer n can be written as n=ax^2+by^3+cz^4+dw^5 and as n=ax_1^2+bx_2^3+cx_3^4+dx_4^5+ex_5^6+ fx_6^7+gx_7^8+hx_8^9+kx_9^10 with x_i in Z and a,b,c,d,e,f,g,h,k in {-1.+1}.
Representations of numbers as sums and differences of unlike powers
JABARA, Enrico
2010-01-01
Abstract
In this paper we prove that every integer n can be written as n=ax^2+by^3+cz^4+dw^5 and as n=ax_1^2+bx_2^3+cx_3^4+dx_4^5+ex_5^6+ fx_6^7+gx_7^8+hx_8^9+kx_9^10 with x_i in Z and a,b,c,d,e,f,g,h,k in {-1.+1}.
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