Online Course Discussion Forum

IIB NT 3.9, 3.10

 
 
LeeClaire的头像
IIB NT 3.9, 3.10
LeeClaire - 2024年03月22日 Friday 17:27
 

Can you explain problem 3.9 and 3.10?

For 3.9, I have no idea..

For 3.10,  why a(n-1, m-1)+b(n,m) is an integer?

 
LensmireJohn的头像
Re: IIB NT 3.9, 3.10
LensmireJohn - 2024年03月26日 Tuesday 19:12
 

Thanks for your patience with our reply. Here's some hints:

- 3.9: For problems like this, try to do the opposite. Try to build a set for as long as possible so that any two numbers chosen are relatively prime. For example, 1 is good to include, as it is relatively prime with everything. Hint: Primes are probably also good to try to include.

- 3.10: By Bezout's Identity, we can replace gcd(m,n) by a*m + b*n for integers a and b. Try to rewrite the expression from here. Hint: We know that $\displaystyle \binom{A}{B}$ is always an integer for any non-negative integers $A$ and $B$, can you take advantage of this?

Hope this helps!

General Note: We do highly recommend students get the textbooks for the live classes. The textbooks do include the solution ideas for all the Example Problems, numbered 1 through 10 of each chapter.