How many digits does the smallest positive integer K have, while satisfying all of the following conditions: • K is an odd number • K is a cube • K is a square • K is divisible by 12 different prime numbers

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Q: How many integers in {1, 2,..., 100} are not divisible by 7 or 5? (Give the exact number)

A: Find the number of integers in 1,2,...,100 which are not divisible by 7 or 5.

Q: Number theory.

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Q: Do you thinkthat there are infinitely many primes of the n -1

A: there are infinitely many primes of the n -1 Explain the above statement

Q: 20. 58 21. 100 22. 60 81 24. 56 23. 25 169 837 (Hint. Perfect square)

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A: Given, if 7 divides n with remainder 1. We have to prove that 7 divides n2+2n+7 with remainder 3.

Q: Which of the following is a prime number? A O 33 BO O:

A: The objective is to find the prime number.

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Q: Use the Fermat's method to express each number in canonical prime factorization. 1. 229 2. 383 3.…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: If p and q are twin primes, then which of the following is true. i. p + q is divisible by 3 ii. pq…

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Q: Show that 3 is a factor of n3 + 2n for all natural numbers n. Let P denote the statement: 3 is a…

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Q: 2. What are the two largest positive integers n satisfying n - 1 | n²-A?

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Q: For each natural number n A, = (-→ 3+n U-1 Find UneN An and NnEN An

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Q: Suppose that n is a positive integer with the properties: • for any integers a, b, c, • n is not…

A: Suppose that n is a positive integer with the properties:1). for any integers a, b, c    2). n is…

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Q: Consider the set of positive integers A = {9n+1: n = Z, n ≥ 0} We call an element of A prume if it…

A: Here Set A is A={10,19,28,37,46,55,64,73,82,91,......}Prime elements of A={19,37,73,....} To find…

Q: 9. Let n be an odd number with exactly four distinct prime factors. If (3, n) = 1, prove that n is…

A: We will use knowledge of number theory to answer this question.

Q: Find the largest negative integer leaves a remainder 2 when divided by 3, 5, and 12. (If it is not…

A: Let us  solve the question in the next step.