Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

still couldn't solve the problem... can you show me how to prove it?

**gourish**- Replies: 2

here is a question that i came across in a competition (math crusade 2014) which i couldn't answer

Q.) if the nth term of the Fibonacci sequence: 1,1,2,3,5,8,13..... is represented by Fn then for n greater then 4 and being a composite number

prove that Fn is a composite number

if you guys can show me the way i can walk the path.... like how should prove that a given number is composite when i cannot even have any idea of what it's factors may be...

thanks for sharing... i bet bobbym is a professor isn't he?

ok... well i read that it contains graph theory... why is that necessary for combinatorics?

so any suggestions for a good book that i can read for combinatorics... including such problems...

36... the answer...

i bet you didn't expand that term by hand....

okay so we now get to back the question that u originally asked me.... right... we now need to find the coefficient of x^10 in this expansion where the whole term is raised to 3....

now getting back to the multinomial theorem....(i have got a fair enough idea of binomial theorem and have read that multinomial theorem is general form of bi theo..)

okay.... go on... i have the polynomials representing the variables...

well that's just choosing 2 spaces out of 9.... cool i got it it's (9 chooses 2)... brilliant...

umm... take x_xxxxxx_xxx_xxx.... so there are groups (x) (xxxxxx) (xxx) (xxx).... let a=(x) b=(xxxxxx) c=(xxx) d=(xxx)..

the sum of these groups or variables is 13. and i took the c and d as the same as there is no constraint like a,b,c,d are distinct....

yeah... i get it.... so these variables (groups)

if the first thing is what ur asking me to do then it's 12

they are greater then 3 but less then 4 in each group of x's @bobbym