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Post Closed as "Needs details or clarity" by Ben McKay, Henry.L, R.P., Stefan Waldmann, Mikhail Katz
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mingming
mingming
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Solution to $ \sum (-1)^k \binom{n}{k} \alpha_k = a$b_n$?

Is there anyone can tell me any information about the integer solution to the combinatotial equation $$ \sum (-1)^k \binom{n}{k} \alpha_k = a $$$$ \sum (-1)^k \binom{n}{k} \alpha_k = b_n $$ (all variables are integers)? For example, suppose alpha_{0}=0 , when n=2, it is 2alpha_{1}-alpha_{1}=-b_{2} If we take b_{2} to be a given number, this is a first degree Diophantine Equation, we know how to solve it using elementary number theory, right? But when n=3, take b_{3} to be a given number, alpha_{0}=0, could you write down a general solution to this Dioph. equation? Thank you very much!

Solution to $ \sum (-1)^k \binom{n}{k} \alpha_k = a$?

Is there anyone can tell me any information about the integer solution to the combinatotial equation $$ \sum (-1)^k \binom{n}{k} \alpha_k = a $$ (all variables are integers)? For example, suppose alpha_{0}=0 , when n=2, it is 2alpha_{1}-alpha_{1}=-b_{2} If we take b_{2} to be a given number, this is a first degree Diophantine Equation, we know how to solve it using elementary number theory, right? But when n=3, take b_{3} to be a given number, alpha_{0}=0, could you write down a general solution to this Dioph. equation? Thank you very much!

Solution to $ \sum (-1)^k \binom{n}{k} \alpha_k = b_n$?

Is there anyone can tell me any information about the integer solution to the combinatotial equation $$ \sum (-1)^k \binom{n}{k} \alpha_k = b_n $$ (all variables are integers)? For example, suppose alpha_{0}=0 , when n=2, it is 2alpha_{1}-alpha_{1}=-b_{2} If we take b_{2} to be a given number, this is a first degree Diophantine Equation, we know how to solve it using elementary number theory, right? But when n=3, take b_{3} to be a given number, alpha_{0}=0, could you write down a general solution to this Dioph. equation? Thank you very much!

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mingming
mingming
  • 39
  • 4

Is there anyone can tell me any information about the integer solution to the combinatotial equation $$ \sum (-1)^k \binom{n}{k} \alpha_k = a $$ (all variables are integers)? For example, suppose alpha_{0}=0 , when n=2, it is 2alpha_{1}-alpha_{1}=-b_{2} If we take b_{2} to be a given number, this is a first degree Diophantine Equation, we know how to solve it using elementary number theory, right? But when n=3, take b_{3} to be a given number, alpha_{0}=0, could you write down a general solution to this Dioph. equation? Thank you very much!

Is there anyone can tell me any information about the integer solution to the combinatotial equation $$ \sum (-1)^k \binom{n}{k} \alpha_k = a $$ (all variables are integers)? Thank you very much!

Is there anyone can tell me any information about the integer solution to the combinatotial equation $$ \sum (-1)^k \binom{n}{k} \alpha_k = a $$ (all variables are integers)? For example, suppose alpha_{0}=0 , when n=2, it is 2alpha_{1}-alpha_{1}=-b_{2} If we take b_{2} to be a given number, this is a first degree Diophantine Equation, we know how to solve it using elementary number theory, right? But when n=3, take b_{3} to be a given number, alpha_{0}=0, could you write down a general solution to this Dioph. equation? Thank you very much!

clarified meaning and smartened up Latex; edited title
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Tom Leinster
Tom Leinster
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Solution to $ \sum (  -1  )^{k}\{^^k \binom{n}_{k}\}\alpha_{k} \alpha_k = a $a$?

Is there anyone can tell me any information about the integer solution to thisthe combinatotial equation   $$ \sum (-1)^k \binom{n}{k} \alpha_k = a $$ ( allall variables are integers  )? Thank you very much!

Solution to $ \sum (  -1  )^{k}\{^{n}_{k}\}\alpha_{k} = a $?

Is there anyone can tell me any information about the integer solution to this combinatotial equation  ( all variables are integers  )? Thank you very much!

Solution to $ \sum (-1)^k \binom{n}{k} \alpha_k = a$?

Is there anyone can tell me any information about the integer solution to the combinatotial equation $$ \sum (-1)^k \binom{n}{k} \alpha_k = a $$ (all variables are integers)? Thank you very much!

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mingming
mingming
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