For every natural number n, one of n-1, n, or n+1 is a multiple of 3

Q: How many integers from 1 to 700 (inclusive) are divisible by the factors of 70 greater than 1?

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Q: Take any arbitrary integer n and then square it, which one is true? n2 cannot be in the form 7k + 5.…

A: Solution is given as follows :

Q: n(nº +5) is divisible by 6, for each integer n 0.

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Q: Compute for an arbitrary integer k

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Q: Prove that 5 does not divide 5n+3 for any integer n.

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Q: Show that an integer N is divisible by 9 if and only if the sum of its digits is divisible by 9

A: Let a=anan-1...a3a2a1 be an integer and S be the sum of the digits. Consider a,…

Q: Use induction to show that n4 + 15 is a multiple of 16 for every positive odd integer n.

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Q: Covert to an equalivent statement to a universal statement:"6 is the smallest postive integer that…

A: According to the given information, It is required to write the statement into universal statement.…

Q: How many triples of integers from 2 through 16 can be formed in which the integers are in increasing…

A: Any triple of integers (i, j, k) with 2 ≤ i ≤ j ≤ k ≤ 16 can berepresented as a string of 15 – 1…

Q: Number theory.

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Q: Prove that an odd number multiplied by an odd number is odd.

A: The objective is to prove that an odd number multiplied by an odd number is odd.

Q: Show that for every positive

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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: Show that for any integer n > 5, the integers n, n+2, and n +4 cannot all be primes.

A: Lets prove by contradiction Lets say integers n, n+2 and n+4 are all prime number for some integer…

Q: If a is any integer, is a(a + 1) even or odd?

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Q: Use mathematical induction to prove that 3n+ 7n−2 is divisible by 8 for every non-negative integer…

A: The given statement is, Pn=3n+7n-2 Let us assume that the statement is true for n=1 P1=31+71-2=8 As…

Q: what two consective odd integers have a product of 63?

A: Find two odd integers.

Q: let n be an integer solution to the equation n2+an-b=0 (n>7) if the representation of a in base n is…

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