5) Let n be a positive integer such that 7 | (8-1). Prove that 7 | (8=*1 - 1). (Hint: Rewrite 8*1 -1, where a portion of the expression is 8 times 8ª - 1.)

Q: Prove that (-1ti3)" + (-1-is3)" has either the value 2n+' or the value -2" if r is any ). integer…

A:

Q: 16 M = 7 -5 Find formulas for the entries of M", where n is a positive integer. M" =

A: We have to find the entries of matrix Mn.

Q: Select two positive integers a and b with 5 <  a  ≤  20  and 5  <  b ≤  20.

A:

Q: Prove that 7^n − 1 is a multiple of 6 for all n ∈ N. ( N is Natural Number)

A: Advance maths

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: How many positive integers less than 10000 are there which contain at least one 7 or at least one 9…

A:

Q: Let n>,2 and k be any boretine Proce that integers (n-1)* | n, 2

A: Given, n≥2 and k is any integer. n≡1modn-1Therefore, ni≡1modn-1 ∀i∈ℕ…

Q: n^2 +1 is not divisible by 3 for every integer n.

A: Any integer n can be written in the form of: n=3a+b, where b = 0 or 1 or 2 Case 1: If b=0, n2+1=…

Q: what is the counter example for all numbers x,      x + x    >  x

A:

Q: 8. If * is defined as a*b = 3a+b where a and b are real numbers, what is 4*3?

A: Given operation is a*b = 3a+b

Q: Prove 3 | 17k+1-2*5k+3+11k+3 for k>=0 (nonnegative integer)

A: Here in this problem we have to prove that for k≥0 i.e k is a non negative integer…

Q: If a,b,c,d are in distinct real number in A.P. Such that 2(a-b)+c(b-c) +(c-a) =2(a-d)+(b-d) +(c-d)'…

A:

Q: Prove that la + b + c| < ]a] + ]b| + |c[

A: Prove that,    a+b+c≤a+b+c

Q: If a and b are positive integers, which of the following can never be the gcd(56a, 63b)? (а) 56а (b)…

A: given a and b are positive integers,  and to find gcd(56a, 63b) gcd of (56, 63) is 7  so gcd(56a,…

Q: 4 (ii) 16 | at + 15.

A: Step-1 1)16|a4+15

Q: Given:<His a right angle, HK = HI GL= LJ, and KL = LI Prove: AHGI AHJK Statements ZHis a right…

A:

Q: Help please Disprove the statement  by giving a counterexample :…

A: The given statement is a mathematical proposition that states: For all real numbers a and b, if a is…

Q: (b) Prove that 27 (2⁹⁹ +1).

A:

Q: let a,b,c,d,e and f be different positive integers so that a² - b² = c² - d² = e² - f² = 63. Value a…

A: Given:- a,b,c,d,e and f are different positive integers.  also a2-b2=c2-d2=e2-f2=63. To find :- the…

Q: 6. Prove by CVI that every natural number n > 2 is a product of prime numbers. NOTE. A prime number…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Prove that 1+6x-x is always a positive real number if x =3+Ai for some real 33 number 4

A: The given number is  1 + 6x - x2

Q: Use the contraposition to prove:  If n^2 + n + 1 is an even integer, then n is an odd integer

A: Step 1:  Step 2: Step 3: Step 4:

Q: sing direct proof, prove the following statements: 1. Prove: If x2-4=0, then x = 2 or x = -2. 2. If…

A: follow next step

Q: Prove that the statement is true for every positive integer n.

A: We know that the sum of a geometric series of the form: a+ar+ar2+ar3+...........+arn-1 with the…

Q: 6) Let n be a positive integer such that 7 | (52n-1 +22n-1). Prove that 7 || (52n+1+22n+¹). (Hint:…

A: Since, given that  52n-1+ 22n-1  is divisible by 7 .  We have to prove that  52n+1+22n+1 is also…

Q: Prove by cases For any integer n, n^2 + 5 is not divisible

A:

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

A:

Q: Prove that 8 | (54" +7) for every positive integer n.

A:

Q: Prove that if  n  is a positive integer, then  5 | (6^n − 1)

A:

Q: Let k be an positive integer. Prove that k(7k^2 + 5) + 6 is divisible by 6

A: Let k be an positive integer. Prove that k(7k^2 + 5) + 6 is divisible by 6

Q: Prove that 6">5" + 9 for any integer n ≥ 2.

A: Mathematical induction is a technique used to prove statements about well-ordered sets of natural…

Q: Use proof by contradiction to show that there is no positive real number x such that (x-2)/x ≥…

A: In an inequality, if a positive number is multiplied then there is no change of sign of inequality.…

Q: If a and b are integers with gcd(a, b) = d Then a gcd %3D -1

A: False.

Q: a.Given an integer a, then a² + 4a + 5 is odd if and only if a is even. b. There exists a positive…

A: Since you have posted multiple subpart questions, we will solve the first three questions for you.…

Q: Show that yn for all n=1, 2₁- ✓

A:

Q: 2. When the expression (156)(205) (557) is evaluated, it ends with a string of consecutive zero's.…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.