This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Questions for the exam 1 Theoretical questions 1. Formulate binomial theorem. Right the formula for ( x + y ) n and formula for the binomial coefficients. 2. For two positive integer numbers n,m define gcd ( n,m ) and prove that it exists. You can not use prime number factorization, you can use well ordering principle. 3. For two polynomials n ( x ) ,m ( x ) define gcd ( n ( x ) ,m ( x )) and prove that it exists. 4. Prove that if integers numbers a and c are relatively prime and c divides ab then c divides b . 5. Prove that if polynomials a ( x ) and c ( x ) are relatively prime and c ( x ) divides a ( x ) b ( x ) then c ( x ) divides b ( x ). 6. Prove that there are infinitely many prime numbers. 7. Prove that if a product of several numbers is divisible by a prime number p then one of them is divisible by p . 8. Prove that if a product of several polynomials is divisible by an irreducible polynomial p ( x ) then one of them is divisible by p ( x )....
View Full
Document
 Spring '08
 MULLEN
 Math, Binomial Theorem, Binomial

Click to edit the document details