Recent content by StellaLuna

Could anyone help me with the following proof? F^2_n + F^2_(n+1) = F_(2n+1) for ngreater than or equal to 1?

\sum_{k=100}^{201} \binom{201}{k+1} \binom{k+1}{101} Is what I got after using the hockey stick identity. I then carried out both combinations but was not sure how to rearrange them after?

I'm looking for an expression involving one or two binomial coefficients. And yes j starts at 100

Thank you for responding, I still don't quite know how to even start what you suggested.

I'm quite stuck with how to approahc this type of question. Σ(k=100 to 201) Σ(j=100 to k) (201 over k+1)(j over 100) Sorr for the set up, it is tricky to type. The brackets indicated a combination.

I was wondering if someone could help me with a proof. If ab<0 (can we assume that either a or b is negative then?) and d(gcd of a and b)│c, there there is at least one solution of ax+by=c with x and y positive.