10. Show that among 7 randomly chosen integers, there must be 2 whose difference is divisible by 6.

Q: Explain why, in any set of 11 positive integers, some two integers must have the same I's digit.

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Q: Determine how many eight-digit positive integers you can make if the integers must include at least…

A: Let us assume there are three persons A, B and C sitting beside each other. The different ways in…

Q: How many 6-digit positive integers are divisible by 3 but not by 9 or by 10?

A: Sol:- For a number to be divisible by 3, the sum of its digits must be divisible by 3. Let's…

Q: Determine the number of integers between 1 and 10000 that are not divisible by 6, but are divisible…

A: Given, the number of integers between 1 and 10000 To find the integers between 1 and 10000 that are…

Q: Show that a number with 30 digits cannot have more than 100 prime factors.  

A: Prime factor: A factor of a number which is a prime number. For example: consider a number 26. The…

Q: a) Find the number of positive integers not exceeding 120 that are divisible by 3 or 4.

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Q: Factor 10k + 1 into a product of primes for k = 1, 2, 3, 4, 5.

A: The main objective is to factor p(k)=10k+1 into product of primes for k=1,2,3,4,5.

Q: What is the number of positive integers not larger than 210 and not divisible by 2, 3 or 7?…

A: Within 210, the number of integers that are divisible by 2= 210/2= 105  Within 210, the number of…

Q: How many integers between 1 and 1000 are divisible by 3, 5, 11, or 13?

A: We have to find the total  integers between 1 and 1000 are divisible by 3, 5, 11, or 13. First find…

Q: Find 1000 consecuticve composite integers. (Do not write them out).

A: To find :  The  1000 consecutive composite integers.      Formula Used :   The n consecutive…

Q: Find the number of positive integers not exceeding 104 that are not divisible by 5 or by 7.

A: In this Question we have to find the number of positive Integer between 0 and 104 which is not…

Q: 10. Find the sum of the coefficients of (2x– 3)°. c. -6560 d. -5120 а. -5660 b. -6780

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Q: Find the smallest number greater than 200 with 14 positive divisors

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Q: Find an integer between 100 and 150 divisible by 9.   How do i figure this out, I am completely…

A: A number is divisible by 9 if the sum of the digits is divisible by 9.

Q: Find the smallest integer greater than 100 that is divisible by 5, but leaves the remainders 1, 5…

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Q: How many distinct ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2 orange marbles…

A: Given problem:- How many distinct ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2…

Q: How many positive numbers less than 300 are divisible by 7 but not 5?

A: We need to find positive numbers less than 300 that are divisible by 7 but not by 5. First count the…

Q: 5. Find the number of positive integers less than 700 that are divisible by 3 but not divisible by…

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Q: Determine the number of integers between 100 and 500 that are divisible by 7

A: We have the integers between 100 and 500 that are divisible by 7 are 105, 112, 119, ........, 497

Q: 3. Find the greatest common divisor and least common 2338712132 and b = 365511²13. multiple of a =

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Q: Compute P9,2. (Enter an exact number.)

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Q: Find the largest positive integers that will divide 398, 436 and 542 leaving emainders 7, 11 and 15…

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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: that the set of negative integers divisible by 3 is countable

A: Set of negetivee integers divisible by 3 isS=-3n, n∈ℕf: ℕ→S   defined asf(n) = -3n,To check…

Q: List the integer of the elements of B = {7, V7, –20, 0, –, 1.5, /16 8 55

A: Solution set has four elements as per the given condition Explanation is given below

Q: 1) Find the number of positive integers not exceeding 100 that are not divisible by 5 or

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