首页|期刊导航|哈尔滨工业大学学报（英文版）|Solvability of the Diophantine equations xp + 22m y4 = pk z2 and xp + y2 = pk z4
哈尔滨工业大学学报（英文版）2002，Vol.9Issue(2)：107-109,3.
Solvability of the Diophantine equations xp + 22m y4 = pk z2 and xp + y2 = pk z4
Solvability of the Diophantine equations xp + 22m y4 = pk z2 and xp + y2 = pk z4
摘要
Abstract
We study the solvability of two classes of Diophantine equations by using some new methods and new results in this paper.Letp be an odd prime and Bn denote nth Bernoulli number.We prove that ifp ≡ 1(mod 4)andp |B(p-1)/2,then the equationxp +22mn4 = pky2,m,n,k ∈ N ,k ＞ 1,gcd(x,py)= 1,and the equationxp +y2 =pkz4,k ∈ N,gcd(x,y)= 1,k ＞ 1,21 y have no integral solutions respectively.关键词
exponential Diophantine equation/solvability/public key cryptosystemsKey words
exponential Diophantine equation/solvability/public key cryptosystems分类
数理科学引用本文复制引用
..Solvability of the Diophantine equations xp + 22m y4 = pk z2 and xp + y2 = pk z4[J].哈尔滨工业大学学报（英文版）,2002,9(2):107-109,3.基金项目
Sponsored by the National Natural Science Foundation of China(Grant No.60072018). （Grant No.60072018）
