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Results tagged with diophantine-equations
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user 31236
Diophantine equations are polynomial equations $F=0$, or systems of polynomial equations $F_1=\ldots=F_k=0$, where $F,F_1,\ldots,F_k$ are polynomials in either $\mathbb{Z}[X_1,\ldots,X_n]$ of $\mathbb{Q}[X_1,\ldots,X_n]$ of which it is asked to find solutions over $\mathbb{Z}$ or $\mathbb{Q}$. Topics: Pell equations, quadratic forms, elliptic curves, abelian varieties, hyperelliptic curves, Thue equations, normic forms, K3 surfaces ...
6
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answers
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Are twin primes the only solution to this equation?
Let $p,q_i, i \ge 1$ be primes, $m$ a positive integer.
The equation
$$
p.\prod_{i=1}^m(q_i-1)-(p-1).\prod_{i=1}^mq_i=2
$$
for $m=1$ has all twin primes $p,q_1=p+2$ as solution.
Are there solutions …
- 343