On the generalized Ramanujan-Nagell equation $$\pmb {x^2+(3m^2+1)=(4m^2+1)^n}$$
Tóm tắt
Let m be a positive integer. Using certain properties of Pell equations with elementary number theoretic methods, we prove that the equation
$$x^2+(3m^2+1)=(4m^2+1)^n$$
has only two positive integer solutions
$$(x,\ n)=(m,\ 1)$$
and
$$(8m^3+3m,\ 3)$$
.
Tài liệu tham khảo
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