Show that in any collection of 7 or more natural numbers there are ALWAYS TWO numbers whose sum or difference is divisible by 11.

Q: Find the sum of the first 80 positive even integers.

A: 2, 4, 6, 8, 10,....... This is an arithmetic sequence with  a1=first term=2d=common difference=4-2=2…

Q: How many distinct expressions exist for the number?

A: The concept of "distinct expressions" for a number can vary depending on what you mean by it. Here…

Q: A "S number" is a positive even number that is not the product of two even numbers. A "B number" is…

A: Given: S number= positive even number that is not the product of two even numbers,  B number=an…

Q: Find the value of a + b + c + d. (Answer must be an integer) The Differential Equation 2y"' + 3y" –…

A: Let us consider a differential equation L(D)(y)=Q(x) Determine the complementary solution by using…

Q: Any n consecutive integers will include a number that is divisible by n.

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Q: For two or more natural numbers, how does the greatest common divisor and least common multiple…

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Q: let a = 3^4 7^3 11^2 13^5 and b = 2^6 5^2 7^2 11^3 13^4 Determine the values of (a,b) and [a,b] and…

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

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Q: Show that n-lis divisible by 8, if n is an odd positive integer

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Q: Which integers leave a remainder of 1 when divided by 2 and also leave a remainder of 1 when divided…

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Q: show that every integer greater than 11 is the sum of two composite integers

A: We need to prove that  every integer greater than 11 is the sum of two composite integers.

Q: What is the sum of the first 100 nonnegative integers?

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Q: m Additional Materials eBook Submit Answer MY NOTES x cm 15. [-/1 Points] DETAILS ISM Meters. How…

A: We will find the required.

Q: Find out how many distinct three-digit numbers can be formed using al the digits of 1, 2, and 3. * O…

A: To find  Number of distinct three digit numbers can be formed using all the digits 1,2 and 3.

Q: When a whole number is multiplied by 100, where is there a 0 in the product

A: Given:Whole number is multiplied by 100,Where is there a 0 in the product

Q: Show that every odd integer is the sum of two consecutive integers

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Q: Which integers are divisible by 5 but leave a remainder of 1 when divided by 3?

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Q: How many negative divisors has the integer 90?

A: The divisors of 90 are all the numbers that we can evenly divide into 90.

Q: ntegers not exceeding

A: Principal of Inclusion-Exclusion:                 A∪B∪C=A+B+C-A∩B-A∩C-B∩C+A∩B∩C Here A, B, C denote…

Q: Find five consecutive odd integers such that when the fifth is subtracted from eigt times the…

A: We're going to solve

Q: Write the number 240 as a sum of three numbers so that the sum of the products taken two at a time…

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