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New posts in pell-type-equations
Link between the negative pell equation $x^2-dy^2=-1$ and a certain continued fraction
number-theory
diophantine-equations
continued-fractions
pell-type-equations
Pairs of $(p,q)$ such that $p^2 + 1 = 2 q^2$?
number-theory
algebraic-number-theory
diophantine-equations
pell-type-equations
Solutions to the Pell equation $(2x+y)^2-5y^2=4$
abstract-algebra
number-theory
elementary-number-theory
pell-type-equations
algebra direct connect pell eqn soln $(p_{nk},q_{nk})$ with $(p_n + q_n\sqrt{D})^k$
continued-fractions
pell-type-equations
Solving $X^2-6Y^2=Z^3$ in positive integers
elementary-number-theory
diophantine-equations
cubics
pell-type-equations
How to find a fundamental solution to Pell's equation?
pell-type-equations
Pell number factorization and divisibility question
elementary-number-theory
systems-of-equations
divisibility
pell-type-equations
Do I catch all solutions for the generalized Pell-equation $a^2+b^2 = 2 c^2$ by this matrix-method?
number-theory
elementary-number-theory
pell-type-equations
On $\big(\tfrac{1+\sqrt{5}}{2}\big)^{12}=\small 161+72\sqrt{5}$ and $\int_{-1}^1\frac{dx}{\left(1-x^2\right)^{\small3/4} \sqrt[4]{161+72\sqrt{5}\,x}}$
calculus
integration
definite-integrals
pell-type-equations
Closed-forms for $\int_0^\infty\frac{dx}{\sqrt[3]{55+\cosh x}}$ and $\int_0^\infty\frac{dx}{\sqrt[3]{45\big(23+4\sqrt{33}\big)+\cosh x}}$
calculus
integration
definite-integrals
hypergeometric-function
pell-type-equations
Which triangular numbers are also squares?
elementary-number-theory
diophantine-equations
square-numbers
pell-type-equations
A question about principality of ideals dividing $(p)$ in imaginary quadratic field
algebraic-number-theory
pell-type-equations
Primes in solutions to Pell-type equations
number-theory
elementary-number-theory
pell-type-equations
Let $k$ be a postive integer number . Then $2k^2+1$ and $3k^2+1$ cannot both be square numbers.
number-theory
diophantine-equations
pell-type-equations
A System of Simultaneous Pell Equations
number-theory
diophantine-equations
pell-type-equations
If $(m,n)\in\mathbb Z_+^2$ satisfies $3m^2+m = 4n^2+n$ then $(m-n)$ is a perfect square.
elementary-number-theory
diophantine-equations
pell-type-equations
Does this system of simultaneous Pell-like equations have any non-trivial positive integer solutions?
elementary-number-theory
diophantine-equations
systems-of-equations
pell-type-equations
How to find integer solutions to $M^2=5N^2+2N+1$?
number-theory
diophantine-equations
pell-type-equations
Whenever Pell's equation proof is solvable, it has infinitely many solutions
elementary-number-theory
diophantine-equations
pell-type-equations
Solve the Diophantine equation $ 3x^2 - 2y^2 =1 $
elementary-number-theory
diophantine-equations
pell-type-equations
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