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Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?

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#elementary-number-theory #diophantine-equations
351
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Find $a,b,c$ such that the equation $ax^2+a=by^2+b=cz^2+c$ has infinitely many integer solutions

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#number-theory #elementary-number-theory #diophantine-equations
952
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Is $n(n+1)$ ever a factorial?

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#number-theory #diophantine-equations
417
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Transform quadratic ternary form to normal form

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#diophantine-equations
163
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On $x^3+y^3+z^3 = 1$ and a Pell equation

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#elementary-number-theory #polynomials #diophantine-equations
128
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Find $x \in \mathbb Z^+$ such that $x\sum _{i=1}^{x} \frac 1{i!} \in \mathbb Z$

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#number-theory #elementary-number-theory #diophantine-equations
69
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Why does a Norm Form have rational coefficients?

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#number-theory #algebraic-number-theory #diophantine-equations #normed-spaces #diophantine-approximation
2.5k
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Number of non-negative integer solutions for linear equations with constants

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#linear-algebra #combinatorics #diophantine-equations #generating-functions
3.2k
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Diophantine Equation: $xy+ax+by+c=0$

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#diophantine-equations
3.6k
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At least one member of a pythagorean triple is even

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#elementary-number-theory #diophantine-equations #square-numbers #sums-of-squares #pythagorean-triples
4.8k
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Erdős-Straus conjecture

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#number-theory #reference-request #diophantine-equations #conjectures
148
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How many solutions are possible to the equation $a^x-b^y=c$?

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#number-theory #elementary-number-theory #diophantine-equations
320
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integer solutions of $a^3 + b^2 = 100000$

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#elementary-number-theory #diophantine-equations
203
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Solving a particular system of Diophantine equations in $n$ variables (Frobenius equations)

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#diophantine-equations #computational-complexity #computational-mathematics
257
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Equation representing all numbers

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#diophantine-equations

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