If product of two consecutive odd integers is 63, then the integers are: 7, 9 9, 11 7, 11 7, 13

Q: if 3 does not divide n then 3 divides 2n^2+1

A: Let us Assumue 3 divides (2n2+1) n2+1=3λ Now  2n2+1=n2+1+1⇒(2n2+1)+(-λ)3=1⇒ gcd(2n2+1,3)=1…

Q: 7 8. The sum of two consecutive even integers is of their product. Find these integers. 24

A: Topic- basic maths

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: Determine whether it is possible to express 1 as a liner combination of 1 = m· 44 + n· 91 ,. for…

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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: Give a direct proof of the theorem “The sum of any two odd integers is even”.

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Q: 3. Let z and y be 3-digit numbers such that y is equal to r written backwards. For example, if x =…

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Q: disprove

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Q: Prove or disprove formally and precisely that the product of two consecutive integers is always even…

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Q: A whole number is a perfect number if the sum of its factors​ (other than the number​ itself) is…

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Q: rix with even mumber of permuta Q4. If all elements of A and A are integer numbers, what are the…

A: Let A be any n×n Matrix with integer entries

Q: Deduce expressions for the sum of the first 2n positive integers and the sum of the first n positive…

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Q: If n is an integer and n 2 1, then the expression 4" + 4-1.3+42.3+ 4-.3+4".3++4 3+ 3 is equal to

A: (c) is correct We have to find the value of 4n+4n-1·3+4n-2·3+4n-3·3+4n-4·3+⋯+4·3+3

Q: The factorial of n is the product of all positive integers less than or equal to n. It is…

A: Note:Hey there! Thank you for the question! We have solved this problem using trial-and-error…

Q: The three digit number is given . The sum of all different three digit numbers with the same digits…

A: The three-digit-numbers that satisfies the given property are 108,126,135,234,207,306,405 So there…

Q: Find, If possible, A + B, A- B, 2A, 2A - B, and B +A. (If not possible, enter IMPOSSIBLE In any…

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Q: How many numbers between 1 and 10000 have the digits 1,3, and 5 such that each digit appears exactly…

A: Here Numbers between 1 and 10,000 have digits 1,3,5 and each appears exactly once only

Q: 11.) The sum of four consecutive even integers is 68. Find the four consecutive even integers. What…

A: We know that an even integer is always divisible by 2. Let the first even integer in the consecutive…

Q: If the product of two integers is 2'3*5?7!" and their great- est common divisor is 2°345, what is…

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Q: Is the statement, "If a number is divisible by 2 and 3, then the number is divisible by 6" true or…

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Q: If n = p,P2 ... P where the p, are distinct prime numbers, how many ways can n be written as a…

A: First let us formulate the problem in a different way. Look! we have to find the total number of…

Q: (b) An integer is divisible by 3 if and only if the sum of its digits is divisible by 3.

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Q: Solve by mathematical induction For all integersn> 3, 4(4" – 16) 4 + 4* +4 + .. ……+4" =

A: Solution: The objective is to prove that the given statement using mathematical induction.

Q: Find the sum of all four-digit numbers that can be formed by the digits 1, 3, 5, 7, 9 without…

A: Answer: Option b)  666600

Q: Abby notices that for the first twenty perfect​ squares, each square is either a multiple of​ 5, one…

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Q: а. The sum of the sum of a and b and the quotient of a and b with b as the dividend. a+b b. The…

A: Note as per policy we have to solve only one question at a time, for the remaining questions please…

Q: 5. Given a real number x and a positive integer k, how many multiplications are used to find kx by…

A: Given,A real number x and positive integer kTo find: Total number of multiplications used with the…

Q: 2. Prove the statement: The sum of the squares of any two consecutive integers is odd.

A: I have assumed that n be any integer. Then i have found the sum of square of two consecutive…

Q: Prove: The difference of the reciprocals of two successive integers equals the product of their…

A: Given, 1n-1n+1    We have to prove the difference of the reciprocals of two successive integers…

Q: If a =(2,3,-1) ,(1,6,0) ,(2,1,3) prove that Aa^-1 =A^-1A=I Please show all the step

A: Given matrix is, A=23-1160213

Q: 3. a, =a,,+4", for each integer k21, a, =3 30

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Q: 9) The dimensions of a gift box are consecutive positive integers such that the height is the least…

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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: A positive integer is 4 less than another. If 3 times the reciprocal of the smaller integer is…

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Q: An integer x is odd if x2 is odd. Let x, y and z be integers. If x y and y z, then x | z. For any…

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Q: The three digit number is given the sum of all different three digits numbers with the same digits…

A: Given - The sum of all three digits number that satisfies the given condition = 1998.

Q: a) Consider the digits : 0, 2, 4, 5, 6 , 7. i) How many 4 digits numbers can be formed if repetition…

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Q: 2. Suppose that your scores on the first four tests in a course are 75, 82, 60, and 91. There is one…

A: Given score of four tests is 75,82,60,91

Q: a) Prove that the sum of the squares of two odd integers is always even.

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Q: which

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

Q: difference

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Q: A boy imagined four-digit multiple of 5 with different digits. If the first digit is erased, the…

A: Given that  A boy imagined four digit number If the first digit is erased the obtained number is a…

Q: If m and n are any positive integers and mn is a perfect square, then m and n are perfect squares.…

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Q: Which of the following is the sum of all four-digit numbers that can be formed by the digits 1, 3,…

A: The given digits are 1,3,5,7,9 We know sum of r digits number = n-1Pr-1 Sum of all n digits number…

Q: Prove or disprove that: (a) The product of an odd number with any integer is odd. (b) The sum of two…

A: We know that there are integers with odd and even values, Odd values include-1,3,5,7,9,11,13,15,17,…

Q: A restaurant offers a dinner special that lets you choose from 10 entrees, 8 side dishes, and 13…

A: Multiplication rule of counting:If a task consists of a sequence of choices in which there are ‘a’…

Q: 1.Prove that the product of two consecutive integers is divisible by 2.                   (Use…

A: Product of two consecutive integers is divisible by 2

Q: i) If you have twenty ones and fifteen zeroes how many ways can we arrange these digits such that no…

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

Q: True or False: For all integers a, b, and c, if a divides b and b divides c, then a divides c. True…

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