进一步研究了满足条件 f(u2+kv2)=f2(u)+kf2(v)的数论函数 f(n),证明了其在k=6的情形下可分成3类,进而验证了关于f(n)的猜想在k=6时是正确的. 进一步地,总结了研究过程中出现的一些有趣结果,指出了该数论函数在参数k的不同取值下,其证明过程中出现的一些联系与区别,旨在为猜想的完全证明提供一些可能的理论支撑.
The arithmetic function f(n) which satisfies f(u2+kv2)=f2(u)+kf2(v) is further studied. It is proved that f(n) can be divided into three classes with k=6, and thus the conjecture of f(n) in the case of k=6 is verified. Whats more,some interesting results are presented. Some relations and distinction in the process of the proof with different values of parameter k are pointed out, which aims at providing some possible theoretical support for the complete proof of the conjecture.