# Tagged Questions

Questions on congruences, linear diophantine equations, greatest common divisor, divisibility, etc.

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### Do we have negative prime numbers?

Do we have negative prime numbers? $..., -7, -5, -3, -2, ...$
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### About the sigma function and an interesting inequality. [closed]

Is it true $\sigma(A)$/$\sigma(B)$ > = (A/B) ; given B divides A ?
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### Find the number of integers n such that the equation

Find the number of integers n such that the equation $xy^2+y^2-x-y=n$ has an infinite number of integer solutions $(x,y)$.
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### How many duplication formulas exist for the Mordell curve family $Y^2-X^3=c$?

For the Mordell equation $$Y^2-X^3 = c,$$ Bachet gave a famous duplication formula which translates one rational solution $(x_1,y_1)$ into a second rational solution $(x_2,y_2)$. Réalis gave a ...
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### Does the equation has a non-trivial solution?

Could you give me some hints how I can solve the following exercise? Check if the equation $3x^2+7y^2-5z^2=0$ has a non-trivial solution in $\mathbb{Q}$ . If it has a solution, find at least one. If ...
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### find a parametric solutions for a special equation

Let $a,b,c$ be rational.Find a rational parametric solutions for $a,b$ and $c$ so that simultaneously $$a^2-c^2=\square$$ and $$b^2-c^2=\square$$