4) (-a) (- b) = ab (5) ac = bc ⇒a=b

Q: Expand and evaluate the sum 4 Σ3k +1 k-1

A: Observe that the given expression is the sum of all the terms (3k + 1) where k takes the values from…

Q: Exploring permutations.  The formula for the number of ways to arrange n objects is n! =…

A: No. of parking spots =5 No. of people =5

Q: Verify the formula.

A: Given :2K-2!2k!=12K2K-1

Q: k! k 1

A: Consider the given series

Q: how do you find the following GCD? gcd(n, 2n) where n is a prime integer

A:

Q: Show that if n is odd and 3 n, then n2 = 1 (mod 24).

A: The solution is below.

Q: c) Suppose that 20 students take your discrete math final. The test is worth 150 points, so possible…

A: Given that 20 students take discrete math final. The test is worth 150 points, so possible scores…

Q: Evaluate the factorial expression. 11! (11-3)! 11! (11-3)!

A:

Q: 47.) al Let n = P₁ P2... 92 the Prime factorization of n That a ak EN that is, ai 20) Positive…

A:

Q: 24. Show that 1P + 2P + 3P + .+ (p - 1)P =0 (mod p) when p is an odd prime. Show that if nis prime…

A: Using Wilson's Theorem, Fermat's Little Theorem and The Pollard Factorization Method, we have to…

Q: Select the correct choice that completes the sentence below. The formula for the number of…

A: We want tell you which one is the correct choice.

Q: From a club of 23 people , in how many ways can a group of four members be selected to attend a…

A:

Q: Write a (formal) proof of the following statement: "If 4 does not divide an integer n, then does not…

A: Here we have to prove if 4 doesn't divide an integer n, then 4 doesn't divide n2 -3n+5.

Q: A class consists of 10 boys and 20 girls. In how many ways can this class choose a committee of 2…

A: Combination is the arrangement of data in an ordered way that used to estimate the possible number…

Q: 28. Show that if p and q are distinct primes, then p-1+qP-=1 (mod pq).

A: To prove: If pand q are distinct primes then, pq-1+qp-1≡1(mod pq).

Q: There is an integer n so that 3n² - 10n + 3 is prime.

A: Given: Polynomial: 3n2-10n+3To prove: There is an integer n so that 3n2-10n+3 is prime.

Q: Which of the following is equal to C(200, 50) C(150, 50) О С(200,100) O C(200, 150) O C(150,100)

A: The formula for C(n,r) is evaluated as C(n,r) =n!n-r!·r! C200,50 = 200!200-50!·50! = 200!150!·50!