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Finding Sums of Four Squares via Complex Continued Fractions
Zhaonan Wang, Yingpu Deng
The problem of representing a given positive integer as a sum of four squares of integers has been widely concerned for a long time, and for a given positive odd one can find a…
Supersingular -invariants and the Class Number of
Guanju Xiao, Lixia Luo, Yingpu Deng
For a prime , let be the discriminant of an imaginary quadratic order with . We research the solutions of the class polynomial mo…
On two problems about isogenies of elliptic curves over finite fields
Lixia Luo, Guanju Xiao, Yingpu Deng
Isogenies occur throughout the theory of elliptic curves. Recently, the cryptographic protocols based on isogenies are considered as candidates of quantum-resistant cryptographic p…
Combinatorial Sums $\sum_{k\equiv r(\mbox{mod } m)}{n\choose k}a^k$ and Lucas Quotients
Jiangshuai Yang, Yingpu Deng
In this paper, we study the combinatorial sum $$\sum_{k\equiv r(\mbox{mod }m)}{n\choose k}a^k.$$ By studying this sum, we obtain new congruences for Lucas quotients of two infinite…
Strong pseudoprimes to the first 9 prime bases
Yupeng Jiang, Yingpu Deng
Define to be the smallest strong pseudoprime to the first prime bases. The exact value of is known for . Z. Zhang have found a 19-decimal-digit number…