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Results tagged with diophantine-equations
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user 520102
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 ...
2
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0
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Question on digital sum of the square of $n$
If we set $f(n)=$ the digital sum of $n$，for example, $f(2024)= 2+0+2+4= 8$.
Are there any $n>375501$ in solutions to the equation $f(n^2)=9,$ except $n=10k$, $n=10^a+10^b+1$, $n=5 \cdot 10^a+1$ or $n …
- 321
3
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Six consecutive positive integers with certain shape
With the analysis from Stanley, Joachim and Max Alekseyev, maybe I can solve my question now.
Because two different integers with the form 4k+2 can not appear in these six numbers, when modulo 4, they …
- 321
12
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4
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Six consecutive positive integers with certain shape
Are there 6 consecutive positive integers, where each of them is a square or the product of a prime and a square ?
If they exist, one of those six integers A will be the product of 2 and a square of a …
- 321