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Results tagged with recurrences
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user 70464
6
votes
1
answer
311
views
$p_n(x,y)=\sum_{i=0}^{n-1}x^{n-1-i}y^{i}$ is always an integer
Does anyone know if the following problem has ever been studied?
Let $a$ and $b$ be two real numbers and consider the polynomial: $$p_n(x,y)=\sum_{i=0}^{n-1}x^{n-1-i}y^{i}$$
where $n$ is a posit …
- 3,153
-1
votes
1
answer
141
views
If $p_n(a,b)$ is a rational number (or integer) for 3 consecutive values of $n$ then every $...
Let $a$ and $b$ be two real numbers and $p_n(x,y)$ the polynomial: $$p_n(x,y)=\sum_{i=0}^{n-1}x^{n-1-i}y^{i},$$ where $n$ is a positive integer.
In a previous post I asked if $p_n(a,b)$ was a rationa …
- 3,153