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math.NT2013★ 3 cited
Perfect numbers and Fibonacci primes
Tianxin Cai, Deyi Chen, Yong Zhang
In this paper, we introduce the concept of -perfect number, which is a positive integer such that . We prove that all the -perfect numbers are of th…
math.NT2013
A New Generalization of Fermat's Last Theorem
Tianxin Cai, Deyi Chen, Yong Zhang
In this paper, we consider some hybrid Diophantine equations of addition and multiplication. We first improve a result on new Hilbert-Waring problem. Then we consider the equation…
math.NT2013★ 1 cited
A variety of Euler's conjecture
Tianxin Cai, Yong Zhang
We consider a variety of Euler's conjecture, i.e., whether the Diophantine system \[\begin{cases} n=a_{1}+a_{2}+\cdots+a_{s-1}, a_{1}a_{2}\cdots a_{s-1}(a_{1}+a_{2}+\cdots+a_{s-1})…