We select 38 even positive integers, all less than 1000. Prove that there will be two of them whose difference is at most 26

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Q: Prove that the product of any k consecutive positive integers is an integer multiple of k!.

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Q: Find all integers 100 ≤ n ≤ 999 such that the last three digits of n² is same as n.

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Q: Find the number of positive integers X smaller than 12849 which have exactly 2022 positive divisors

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Q: Prove that 1+1=2

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Q: at any positive odd integer is of the

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Q: The sum of the first n natural numbers, S = 1 + 2 + 3 + first n natural numbers is 171, determine…

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Q: Prove that the sum of any five consecutive positive integers is always a multiple of five.

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Q: Suppose the product of 22 integers is equal to 1. Prove that their sum is not equal to 0.

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Q: Suppose that 75% of students attend lectures for a particular course and 20% of students fall the…

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Q: How many integer solutions to x1 + x2 + x3 + x4 x₁ ≥ 4, x2 ≥ 2, x3 ≥ 5 and x4 ≥ 3? > = 31 are there…

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Q: How many pairs of integers (a,b) exists such that the product of a,b and HCF of (a,b) is 1080??

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Q: n any positive integer n, there exist n consecutive composite integers

A: Given that given any positive integer n, show that there exist n consecutive composite integers.

Q: What is the largest number x such that x<200 and x has exactly 4 factors?

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Q: Let A be the set of all positive integers whose last two digits form a number that is evenly…

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Q: 0, the remainder is 2; and when divided by 11, the remainder is 0. remain is 5; when divided by

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Q: Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5

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Q: Show that if k is a positive integer, then (15k+4)/(10k+3) is in lowest terms.

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