While trying to solve a problem with from STEP questions, I encountered this. I am not sure whether this approach is right for that question but this doesn't look like the right way to approach. Any information would be helpful.
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what is "this" approach? perhaps you meant to have a hyperlink? – R_D Oct 19 '15 at 08:50
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What is the denominator in 1/(1-x^10)(1-x^5)(1-x^2)(1-x)? – A.Γ. Oct 19 '15 at 08:51
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2Use $\frac{1}{1-y} = 1 + y + y^2 + y^3+....$ and then just count who will give you the required index. – Shailesh Oct 19 '15 at 08:52
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@A.G. 1 is the numerator and the rest is in the denominator. Thanks – Abu Bardewa Oct 19 '15 at 08:55
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@Shailesh sorry – Abu Bardewa Oct 19 '15 at 08:58
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@Shailesh you should probably make that into an answer. – CompuChip Oct 19 '15 at 09:03
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What I did was multiplied the denominator and raise it to the power of (-1). – Abu Bardewa Oct 19 '15 at 09:05
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Sorry @Shailesh can u explain your method clearly please . – Abu Bardewa Oct 19 '15 at 09:06
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Will wait. If no one posts an answer within a day, I will. – Shailesh Oct 19 '15 at 09:07
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1While we wait for Shailesh to find the time you can study generatingfunctionology and some examples such as this, this or this. Plenty of other good examples. – Jyrki Lahtonen Oct 19 '15 at 09:28
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1This is also something that might be interesting in connection with this question. Maybe that coin problem is the origin? – mickep Oct 19 '15 at 09:35
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So will the binomial expansion work if I just substitute a negative number ? – Abu Bardewa Oct 19 '15 at 10:02
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I read one of the results proved bu Euler. – Abu Bardewa Oct 20 '15 at 07:51
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It is that there are as many distinct ways of writing the power n as the sum of postive while numbers as there are using odd whole numbers . – Abu Bardewa Oct 20 '15 at 07:52