TY - JOUR
T1 - On the diophantine equation xp + 22m = py2
AU - Cao, Zhenfu
PY - 2000
Y1 - 2000
N2 - Let p be an odd prime. In this paper, using some theorems of Adachi and the author, we prove that if p ≡ 1(mod 4) and p B(p-1)/2, then the equation xp + 1 = py2, y ≠ 0, and the equation xp + 22m = py2, m ∈ ℕ, gcd(x, y) = 1, p | y, have no integral solutions respectively. Here B(p-1)/2 is (p - 1)/2th Bernoulli number.
AB - Let p be an odd prime. In this paper, using some theorems of Adachi and the author, we prove that if p ≡ 1(mod 4) and p B(p-1)/2, then the equation xp + 1 = py2, y ≠ 0, and the equation xp + 22m = py2, m ∈ ℕ, gcd(x, y) = 1, p | y, have no integral solutions respectively. Here B(p-1)/2 is (p - 1)/2th Bernoulli number.
KW - Adachi's theorem
KW - Bernoulli number
KW - Exponential diophantine equation
KW - Higher degree diophantine equation
KW - Pell's equation
UR - https://www.scopus.com/pages/publications/23044517522
U2 - 10.1090/s0002-9939-00-05517-9
DO - 10.1090/s0002-9939-00-05517-9
M3 - 文章
AN - SCOPUS:23044517522
SN - 0002-9939
VL - 128
SP - 1927
EP - 1931
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 7
ER -