Finite difference with common root [on hold]












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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










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put on hold 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.













  • Out of curiosity, how did you come across this question?
    – Pierre-Guy Plamondon
    Jan 4 at 22:55


















1














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










share|cite|improve this question















put on hold 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.













  • Out of curiosity, how did you come across this question?
    – Pierre-Guy Plamondon
    Jan 4 at 22:55
















1












1








1







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










share|cite|improve this question















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






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share|cite|improve this question













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share|cite|improve this question








edited Jan 4 at 22:51







joaopa

















asked Jan 4 at 22:05









joaopajoaopa

34418




34418




put on hold 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.




put on hold 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.












  • Out of curiosity, how did you come across this question?
    – Pierre-Guy Plamondon
    Jan 4 at 22:55




















  • Out of curiosity, how did you come across this question?
    – Pierre-Guy Plamondon
    Jan 4 at 22:55


















Out of curiosity, how did you come across this question?
– Pierre-Guy Plamondon
Jan 4 at 22:55






Out of curiosity, how did you come across this question?
– Pierre-Guy Plamondon
Jan 4 at 22:55












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