Finite difference with common root [closed]
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Let $finmathbb Z[X]$ with degree $ge2$, injective on an infinite subset $E$ of $mathbb Z$. Is it possible that there exists $ane b$ in $E$ such that the polynomials
$$frac{f(X)-f(a)}{X-a}text{ and }frac{f(X)-f(b)}{X-b}$$
have a commin root in $mathbb C$ ?
Thanks in advance
abstract-algebra algebra-precalculus
asked Jan 4 at 22:05
joaopajoaopa
35118
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closed as off-topic by Austin Mohr, jgon, KReiser, Cesareo, Pierre-Guy Plamondon Jan 6 at 15:58
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Austin Mohr, jgon, KReiser, Cesareo, Pierre-Guy Plamondon
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Let $finmathbb Z[X]$ with degree $ge2$, injective on an infinite subset $E$ of $mathbb Z$. Is it possible that there exists $ane b$ in $E$ such that the polynomials
$$frac{f(X)-f(a)}{X-a}text{ and }frac{f(X)-f(b)}{X-b}$$
have a commin root in $mathbb C$ ?
Thanks in advance
abstract-algebra algebra-precalculus
asked Jan 4 at 22:05
joaopajoaopa
35118
$endgroup$
closed as off-topic by Austin Mohr, jgon, KReiser, Cesareo, Pierre-Guy Plamondon Jan 6 at 15:58
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Austin Mohr, jgon, KReiser, Cesareo, Pierre-Guy Plamondon
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
Out of curiosity, how did you come across this question?
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– Pierre-Guy Plamondon
Jan 4 at 22:55
add a comment |
$begingroup$
Let $finmathbb Z[X]$ with degree $ge2$, injective on an infinite subset $E$ of $mathbb Z$. Is it possible that there exists $ane b$ in $E$ such that the polynomials
$$frac{f(X)-f(a)}{X-a}text{ and }frac{f(X)-f(b)}{X-b}$$
have a commin root in $mathbb C$ ?
Thanks in advance
abstract-algebra algebra-precalculus
asked Jan 4 at 22:05
joaopajoaopa
35118
$endgroup$
Let $finmathbb Z[X]$ with degree $ge2$, injective on an infinite subset $E$ of $mathbb Z$. Is it possible that there exists $ane b$ in $E$ such that the polynomials
$$frac{f(X)-f(a)}{X-a}text{ and }frac{f(X)-f(b)}{X-b}$$
have a commin root in $mathbb C$ ?
Thanks in advance
abstract-algebra algebra-precalculus
abstract-algebra algebra-precalculus
asked Jan 4 at 22:05
joaopajoaopa
35118
asked Jan 4 at 22:05
joaopajoaopa
35118
edited Jan 4 at 22:51
joaopa
asked Jan 4 at 22:05
joaopajoaopa
35118
asked Jan 4 at 22:05
joaopajoaopa
35118
asked Jan 4 at 22:05
joaopajoaopa
35118
35118
closed as off-topic by Austin Mohr, jgon, KReiser, Cesareo, Pierre-Guy Plamondon Jan 6 at 15:58
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Austin Mohr, jgon, KReiser, Cesareo, Pierre-Guy Plamondon
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Austin Mohr, jgon, KReiser, Cesareo, Pierre-Guy Plamondon Jan 6 at 15:58
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Austin Mohr, jgon, KReiser, Cesareo, Pierre-Guy Plamondon
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
Out of curiosity, how did you come across this question?
$endgroup$
– Pierre-Guy Plamondon
Jan 4 at 22:55
add a comment |
$begingroup$
Out of curiosity, how did you come across this question?
$endgroup$
– Pierre-Guy Plamondon
Jan 4 at 22:55
$begingroup$
Out of curiosity, how did you come across this question?
$endgroup$
– Pierre-Guy Plamondon
Jan 4 at 22:55
$begingroup$
Out of curiosity, how did you come across this question?
$endgroup$
– Pierre-Guy Plamondon
Jan 4 at 22:55
add a comment |
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$begingroup$
Out of curiosity, how did you come across this question?
$endgroup$
– Pierre-Guy Plamondon
Jan 4 at 22:55