8. Let n ≥ 2. Prove that (n+1)! + k is composite for k = 2,..., n + 1. This shows that there exist arbitrarily long intervals of composite numbers.

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A: See the attachment

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Q: An integer n > 2 is composite if and only if n doe

A: Given Statement: An integer n > 2 is composite if and only if n does not divide (n - 1)! + 1.…

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Q: 11. (a) What does the symbol n! mean? Find 5!. (b) Define (), and find (2).

A: To find 5! and to find the value of 52

Q: An integer n > 2 is composite if and only if n does not divide (n - 1)! + 1. :Select one True False

A: The solution is given as

Q: ) Prove every integer n >= 7, n! > 3n

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Q: Prove that the summation of three odd integers is odd.

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Q: सिद्ध है कि n! > 3 ^ n सभी पूर्णांकों के लिए n> = 7।

A: हमें दी गई समस्या को हल करना है:

Q: Evaluate 10!/9!, (k + 2)!/k!, and k!/(k + 1)!

A: 10!9!,k+2!k!  and k!k+1!

Q: A is the set of odd number greater than 5 and less than 23 n (A)=

A: A is the set of odd numbers greater than 5 and less than  23

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A: We know that 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are digits in the number system.

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Q: 13. Prove that 6 | (n³-n) for every integer n ≥ 0.

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Q: 16. What is the greatest integer N such that (10 – N) + (16 - N)> 5?

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Q: 1/q + 1/r + 1/p =1/m p, q, r are pr

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Q: Show that 10n <3n for n ≥no. Be sure to find no first.

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Q: Show that:

A: Given, nr+nr+1=n+1r+1

Q: How can the sum of k * (n choose k) = n(2 to the power of n-1) be proven akgebraically ?

A: Step 1: We have to prove that, Now by the binomial theorem, Now, differentiating the both sides of…