If both x and ( ++ ) are positive integers, what is the least possible value of x? 10 120 O 90 O 60 O 30

Q: How many solutions are there to the equation X1 + x2 + x3 +x4 + x5 = 21 %3D where r;, i =1, 2, 3, 4,…

A: Depending upon the type of equation, the number of solution will vary. If a system contains linear…

Q: b.) Show that if a and b are positive integers where a is even and b is odd, then (a,b) = (a/2, b).…

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Q: Suppose a and b are both integers that are greater than 1. What is Icm(a, a*b)? a None of the…

A: We have find the lcm of given numbers.

Q: Determine k so that; is singular.

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Q: If 5|(2a + 1) for some integer a, then 25|(14a² + 19a – 19).

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Q: The product of two integers of the form 6k+5 is of the form 6k+1 Select one: True O False

A: 1. The word integer originated from the Latin word ''Integer'' which means whole. It is a special…

Q: , Let a be a positive integer, where the positive difference of every two digits of a in base 10 are…

A: Here, For 1113,     | 1-1 | =0 , | 1-3 | = |-2| = 2 For 2000,     |2-0|= 2, |0-0|= 0 For 2022,…

Q: what is (a'+b,a+b) Wher e a and b are relatively prime integers that are not both Zero1

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

Q: For any integer n ≥ 1, C(6n, 3n) C(6n, 3n-1). O True O False

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Q: Z+ is the set of positive integers. Let A = {1,2,3), B = {n ∈ Z+ | n is even}, C = {n ∈ Z+ | n is…

A: concept Used: C∩D is the set  containing all elements of C that also in the set D C∪D is the set…

Q: Show via proof that for two positive integers a, b where a 2 b, (use combinations e.g. n choose k)…

A: We shall prove for the given statement. Though it has little ambiguities.

Q: Every positive integer is the sum of at most two squares and a cube of nonnegative integers. O True…

A: consider 0  0=02+02+03 now  1 can be written as  1=02+02+13 now consider 2 2=12+02+13 now consider 3…

Q: b) Prove by contradiction: There exist three consecutive odd integer a, b, and c such that a? + b² =…

A: Explanation: Given that,  3 consecutive odd integers a, b & c. Let us assume m & n are…

Q: (c) Let n be a positive integer and assume that there are integers a and b ab. Show that a < yn or b…

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Q: If a and b are positive integers, which of the following can never be the gcd(56a, 64b)? (а) 56а (b)…

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Q: Give an example of a triple (a, b, c) of real numbers such that abc[a][b][c] = 2021, where [x]…

A: Give an example of a triple (a, b, c) of real numbers such thatabc[a][b][c] = 2021, where [x]…

Q: Find all possible values of P in x^2+10x+P=(x-A)(x-B) if P, A and B are all whole numbers

A: To find all possible values of P in x2+10x+P=(x-A)(x-B) if P,A and B are all whole numbers.

Q: Do not use a calculator in this question. 3 V3 6+2v3 5- V3 p+qV3 6. find the CS CamScanner value of…

A: This question is based on similar parallelogram properties and rationalisation.

Q: If a and b are integers with gcd(a, b) = d Then gcd d' = -1 d/

A: Given a statement

Q: (a) For all integers a, b, and c with a # 0, if a | b, then a | (bc).

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Q: 3. Let r and y be positive integers. 4. Let a, b, c e Z. If c divides a +b,

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Q: If a is any integer, is a(a + 1) even or odd?

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Q: Let a, b be nonzero integers with (a, b) = 1. Compute (a + b, a – b).

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Q: Which of the following statements is (are) true for all positive integers? 1) n' + 2n is divisible…

A: given statement 1)  n3+2n  is divisible by 32) 52n-1  is divisible by 24

Q: Let a and b two positive integers. Then we have that axb LCM(a,b) = GCD(a,b). O True O False

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Q: Find all positive integers a, b such that a | b^2-b+1 and b | a^2-a+1

A: Solution :-

Q: Give an example of a triple (a, b, c) of real numbers such that abc[a][b][c] = 2021, where x|…

A: We need to give an example of a triple (a, b, c) of real numbers such that abcabc=2021. If a, b, and…

Q: If x – 1 is an even integer, which of the following numbers must be odd? I. x(x - 1) II. 3(x - 1)…

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Q: 3. Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1 + an-2 - 5, express an in terms of n.

A: We will solve the problem using recurrence relation

Q: 2. How many positive integer solutions are there to Xị + x2 + x3+ x4 < 100

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Q: Let a, b, and c be positive real numbers, and I = =5§S 2xdzdydx. Then I =

A: Given: I=∫0c∫0b∫0a2xdzdydx To find the integral value the order for the integration is dz dy dx

Q: If a²is an even integer, then a is an even integer. If d = ax + by, then d = gcd(a, b). If d|a + b,…

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Q: How many nonnegative integers a, b, c.2 and d are there that satisfy the equation 1 + + a+b 1 a…

A: Given equation has 4 variables a,b,c,d Sum=1 We can find pairs by the following ways

Q: For all positive integers a, b, where a < b, if a {b, then gcd(a, b) = 1. O True False

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Q: There exists a real number R which is greater than 5 O R= {7, 42,2t, and 97/3) O R= {1, 2, and T/6}

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Q: If m and k are positive integers, then, then Ø(m^k )= *

A: The objective is to state whether the statement is true or false. a) The statement: The quadratic…

Q: 10) If x is an integer that leaves a remainder of 2 when divided by either 3, or 5, but that is…

A: If x is an integer that leaves a remainder of 2 when divided by either 3 or 5, but that is divisible…

Q: which

A: Explanation : a )  Let the three consecutive positive integers will be n, n+1 , n+2. If we sum all…

Q: prove if a and b are both odd integer, then 16/ (a^4) + (b^4) -2.

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Q: 7. How many non-negative integer solutions are there to the equation X1 + X2 + X3 + 4 = 16 such that…

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Q: Vn € Zt [obeb(n, n + 1) = 1]

A: l  let n,n+1 are two consecutive positive integers let  the greatest common divisor i.e…

Q: If g and m are positive integers, then which of the following must be equal to ? m (A) g + 5 m + 5…

A: given  g and m are positive integers

Q: 1. Ifx is an even integer, then x is even.

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Q: 1. Show that the set of integers S = {a² + b2 : a, b € Z} that can be respresented as the sum of two…

A: See the details below.

Q: Show that: (n-2)a2 ~X2 (n-2) o2

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: h >x hɛIA

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Q: For positive integers a, b, c, if a|b then ac b. O True False

A: We have to check whether the statement, "For positive integers a, b, c if a|b then ac|b." is true or…

Q: B={z|z is a integer and -2&lt;Z&lt;0}

A: Given,

Q: M is the set of integers that are greater than -1 and less than 4.

A: M is the set of integers