Suppose n1,n2 are positive integers and gcd(n1,n2) = 1. Then for every integer x, if n1 | x and n2 | x, then n

Q: _If A = Verify that [A-!]" = [A"]¬1 ? l1 2.

A:

Q: 23. For any real number a, a ‡ 0, show that a +1 a +4 a +7 a +5 a+6 a +9 a -2 a +3 and a +8 | = 0, a…

A:

Q: 74. Prove that for any real numbers a and b, |b − a|=|a − b|.

A: Given; a and b are any real numbers Consider, L.H.S=b-aWe can write it as,=b+-a=-1-b+a=-1a-b…

Q: If a and b are integers, then a/b is always a rational number. True False

A:

Q: Find the solution to this recursive relation an = an-1+3, a0=1

A: To Find the solution to this recursive relation an = an-1+3, a0=1

Q: In(x²) = 2 ln(x) for all x True O False

A: ln(x^2) =2ln(x) for all x

Q: For any real number a, a ≠ 0, show that a+4 a+7 a+5 a +8 = 0, a+6 а+9 a+1 a+2 a+3 and 4a7a 5a 8a =…

A: We are required to prove: a+1a+4a+7a+2a+5a+8a+3a+6a+9=0a4a7a2a5a8a3a6a9a=0aa4a7a2a5a8a3a6a9=0

Q: . Let a be a positive number. Prove that for each real number x there is an integer n such that na <…

A:

Q: 3n > n for every positive integer n.

A: Now, since we assumed 3k&gt;k, we can substitute k with 3k in the inequality: 3k+1&gt;3k Since ,…

Q: Ex: Let X₂ [1,2,3,4,5]. I. [0,X, [1], 82.3, 81.23], Y. [3,4,5,6,73 andl T₁: [0, X, [4], [4,633 if A:…

A:

Q: For any integer z, if 3 divides z2, then 3 also divides z.

A:

Q: Find the smallest integer x for which (x4 + 4x)/(x + 2) is O(xx). 01 02

A:

Q: Let a and d be integers. Prove that if d|(8a+7)and d|(5a+4), then d|3

A:

Q: |Let A¡ = [i − 1, i] for all integers i = 1,2,3,4. Find the following. a. A₁. A₂- b. A₁ U A₂ U A3 U…

A: The given set Ai=i-1, i for all integers i=1, 2, 3, 4. We have to find, a) A1, A2, A3, A4 b)…

Q: Show that if x > 0 and |x² – 9| < 2, then |x - 3| < 1.

A:

Q: If α and β are two real numbers, we say that β is equivalent to α if there are integers a, b, c, and…

A:

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

A:

Q: 5. Show that 2 32 3" 31 3" for all positive integers n.

A:

Q: If r and s are real numbers and r < s, then there exists a positive integer t such that r+t = s.…

A:

Q: Let an = an-1+ an-2 with ao = 0, a1 = 1. Show that an is even iff ( if and only if) n is a multiple…

A:

Q: Let a, b and c be integers. Prove that if a does not divide b and a|(b+c), then a does not divide c

A: Let a, b and c be integers.

Q: Reject Ho if |z| > N

A: We know that  Null hypothesis H0. Alternative hypothesis H1.

Q: Prove an+1 = (an2+ 1) / 2 with a1 = 2 is monotonic increasing.

A: Solution:-

Q: 11. Prove that every positive integer n can be expressed in the form n=4k or n=4k+1 or n=4k+2 or…

A:

Q: Prove that 2n + 3n is a multiple of 5 for all odd n € N.

A:

Q: Show that n 1 i2 i=1 <2 - n

A:

Q: Let A be a set of n real numbers. Show that A+ A- A € (n).

A: As per the question we are given a set of n real numbers A and we have to show that : |A + A•A| =…

Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

A:

Q: Indicate the least integer n such that (3x5 + x²)4 = 0(x¹). E

A:

Q: Let = [1, -1, 1], [-2, -1, 3] and = [-1, 2, 2]. Find (u ×7)•w: O-14 07 O 10 Does not exist

A:

Q: 3. Show that all integers n ≥ 2 can be expressed as 2x + 3y for some nonnegative integers r and y.

A: Mathematical induction is a proof technique used in mathematics to establish the truth of a…

Q: Let i be a positive integer and A, = [-i+1,1]. Then U2, A

A: We have to use properties of union in this question.

Q: If all entries of A and A -1 are integers, prove that &lt;let A = 1 or -1. Hint: What is det A times…

A: