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How can Falting's theorem be used to decide whether infinite many rational solutions exist?

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#diophantine-equations
86
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$a+b+c=?$ by having $a^2+160=b^2+5$ and $a^2+320=c^2+5$

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#systems-of-equations #diophantine-equations #natural-numbers
116
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Non trivial solutions for the diophantine $X^2Y+XY^2+XYZ-Z^3=0$

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#number-theory #algebraic-geometry #diophantine-equations #rational-numbers
577
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Solve $abc+bcd+cda+dab=abcd+3$ in $\mathbb{N}$.

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#elementary-number-theory #diophantine-equations
92
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Number of solutions of "n-Pythagorean" equation $x_0^n = x_1^n + \dots + x_n^n$

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#algebraic-geometry #diophantine-equations
306
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Is $x^5+x+5=y^2$ solvable over the integers?

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#number-theory #elementary-number-theory #algebraic-geometry #diophantine-equations #algebraic-curves
327
Views

Markov triples that survive Euler's totient function

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#elementary-number-theory #diophantine-equations #prime-factorization #totient-function
136
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Finding integer values of $n$

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#elementary-number-theory #diophantine-equations
60
Views

For which positive integers $k$ dividing $4p^3$, does the equation $x^3+px=k^2$ has an integer solution in $x$?

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#number-theory #prime-numbers #divisibility #diophantine-equations
123
Views

Solving an equation in $\mathbb N$

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#algebra-precalculus #diophantine-equations
39
Views

Solving modular Diophantine

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#diophantine-equations #cryptography
110
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Natural answers of $(n-1)(n)(n+1)+1=x^2$

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#diophantine-equations #elliptic-curves
88
Views

Solve in integers $y^3-1=x^4+x^2$

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#diophantine-equations #gcd-and-lcm #cubics
91
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Can $7n + 13$ ever equal a square?

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#diophantine-equations
237
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Given finite field projections of a rational, can I find the original rational?

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#linear-algebra #diophantine-equations #finite-fields #chinese-remainder-theorem

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