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. What’s 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.
陈亚菲,尤利华 . 一类数论函数的新进展[J]. 华南师范大学学报(自然科学版), 2018, 50(4): 111-114.
CHEN Yafei,YOU Lihua . Further Research Progress on a Class of Arithmetic Functions. Journal of South China Normal University (Natural , 2018, 50(4): 111-114.