А. If p 2q 5 is a prime number, prove that p2-q? is divisible by 3.

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 132n 3 8 ac? c-B" Türkçe: c,…

A:

Q: 4. Write as a single power first, if possible, and then evaluate. a) 5³ x 5 b) 4⁹ ÷ 47 c) (2¹)² -5 •…

A:

Q: 16. Given an odd integer a, establish that a² + (a + 2)²+(a + 4)² + 1 is divisible by 12.

A:

Q: If n is a positive integer, explain why each prime in the factorization 'n² must occur an even…

A: (a) Let p be a prime number that occurs in the prime factorization of n2.   This implies that p…

Q: 16. All positive integers with negative squares are prime.

A: It is a statement. And it is  vacuously true.

Q: Prove by contraposition the following theorem For integers: if n = 2 m, then n² = 4 m² (i.e., if a…

A: Introduction: Numbers divisible by 4 are those that have zeros or multiples of 4 as the last two…

Q: Exercise 6D Use this Venn diagram to answer Questions 1 and 2. Members of youth club (U) Greg lays…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: highest prime that might need to be checked to find the prime factorization of the number. Then,…

A: We need to determine highest prime that might need to be checked to find prime factorisation.

Q: For which odd primes p is 5 a square modulo p?

A: As we know that  a is Quadratic residue mod p if and only if   a(p-1) /2 =1 mod p . If p and q are…

Q: W found that 2,3,5,7 and 11 are not factors of 211. Can we conclude that 211 is prime? Why or why…

A: To check whether 211 is prime number on not.

Q: 2. Is 1501 a square modulo the prime number 3739? Explain.

A: Step 1: Step 2: Step 3: Step 4:

Q: 7) Use a direct proof to show that: a) The sum of an even integer and an odd integer is odd. b) If n…

A: Use the following concepts, to obtain the required result. An even integer m can be written as a…

Q: 5. Which numbers fall between 3 and 4 on a number line? Select all that apply. (NS.2) 8+ 7 A. 9n В.…

A: We have to find number

Q: How many positive integers between 50 and 100 a) are divisible by 7? Which integers are these? b)…

A:

Q: 3. The GCF of any two distinct prime numbers is 1. (Distinct they are not the same number) means

A:

Q: A taxi company has 10 taxis. Part A On a certain day, only seven taxi drivers show up for work. How…

A: Solution: It is given that the taxi company has 10 taxis.

Q: only d)

A:

Q: Is the following proposition true or false? Justify your conclusion with a proof or a…

A: Check the following proposition, "For each natural number n, if 3 does not divide (n2+2) then n is…

Q: Show that if n is a positive integer, then k+4 n(3n +7) k(k +1)(k+2)¯ 2(n+1)(n+2) k=1

A:

Q: A). For how many three digit numbers (100 to 999) is the sum of the digits even? (For example, 343…

A: Let xyz is there digit number x has choice 1,2,...,9 while y and z has choice 1,2,...9  So that…

Q: 4. Do a direct proof using domain knowledge: An odd integer minus an even integer is odd.

A: Given that: Odd integers and even integers. To show : The odd integer minus the even integer is odd.…

Q: Show that if n is an integer and n³ + 5 is odd, then n is even using a) a proof by contraposition.…

A: Proof by contradiction and contraposition

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.