(a) Show that 1++++ 1 21+, 2n-1 2n whenever n is a nonnegative integer.

Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.…

A: To show the representation of an even integers is 2k and that for odd integer is 2k+1 or 2k-1 by…

Q: (1) What is gcd(31212021 + 3, 31212021 - 3)? I am aware of 3121 is a prime number, and 2021 is…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Given that the expression (n²+n+1) n! can be written as a(n + 2)! + b(n + 1)! + cn! where a, b, c…

A: The main objective is to find the sum value.

Q: how that in the domain of integers of the form a+bsqrt(-17) the factorization…

A: The  objective is to show that 13 is irreducible. The norm of 13 is 13=132=169 So if 13 is reducible…

Q: Take any arbitrary integer n and then square it, which one is true? n2 cannot be in the form 7k + 5.…

A: Solution is given as follows :

Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.

A: integer  which have 2 as one of their factors are called even numbers. The integer  which do not…

Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.…

A: Even number: we say a number 'n' is even if it is divisible by 2. if  'n' is even then it is…

Q: Prove that a number in the form 6k+5,” what I mean is a number in the form of 6 times some integer…

A:

Q: 51|1032n+9 – 7, for any integer n 2 0. O True False

A:

Q: Add the polynomials (10z - 82 7æ³ - 10) + (- 4x + 12a + 7a + 9) | Submit Question

A: Add the polynomials. Solution is given below-

Q: (b) If a, b and c are integers such that b| a and b| c, then b | (2a – 3c).

A: We have to proof

Q: Determine whether the expression is a polynomial or not. A) Polynomial B) NOT a polynomial 7. 2x -x…

A:

Q: Show that (a) 8n −3n is divisible by 5 for all natural numbers n.  (b) n2 −n +41 is odd for all…

A: expansion of (a+b)n = hco an bo + nc1 an-1 b1 +.......... +ncn ao b n

Q: Disprove the statement: There is a real number x such that xº +x* +1 = 2x².

A:

Q: Fill in the blank so that the resulting statement is true. 7x-23 If In = In (x-3), then =x-3. x + 2

A: ln7x-23x+2=lnx-3⇒7x-23x+2=x-3

Q: Theorem: The sum of any even integer and any odd integer is odd. Construct a proof for the theorem…

A: We have to prove the theorem by scrambling the given statements.

Q: Prove that the sum of the squares of two odd integers cannot be the square of an integer.

A:

Q: Prove or disprove: There exists an integer a such that 14 | (3a – 5) and 21 | (2a +3).

A:

Q: Show that 3·4n+ 51 is divisible by 3 and 9 for all positive integersn

A: Consider the provided expression,

Q: 9. 10. What is t divisors?

A:

Q: b using recursive Computing the greatest common divisor of two nonnegative integers a and b with a <…

A: To write the program  (R)

Q: Let n be an integer, use the definition of even to prove that 10n+ 4 is even. 10n+4=0x0 Since is a…

A: Let n be an integer. To prove that for any integer n the number 10n+4 is even. An even integer is…

Q: C. Find the possible values of a so that an + an+1 + an+2+ an+3 + an+4 will be divisible by 11.

A:

Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.…

A: Given the statements: The representation of an even integer is 2k for some integer k. The…