(а) Prove that p(n) p(2n) = if n is odd; 24(n) if n is even. (b) Generalize ç(2n) = 24(n) for all even n by showing that p(mn) = every prime divisor of m is a prime divisor of n. то(п) if

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A: 3n+2 and 5n+3 are relatively prime for every integer n.

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Q: true or false In the domain of Gaussian integers Z[i], the element 17 is Irreducible

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Q: Prove that n3 + 2n is divisible by 3 for all n E N.

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Q: Prove that n² +n is divisible by 2, where n E N.

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Q: 1) Show that for all positive integers x, x! + 1 has a prime divisor greater than x.

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Q: 1. It has been conjectured that there are infinitely many primes of the form n2 – 2. Exhibit five…

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Q: 3. Prove that, Σk() = n2n-¹. k=1

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Q: For any integer n2 1. prove that: (a) 1+2+3+..+ (n – 1) + n + (n – 1) + . .. +3+2+ 1 = n². (b) +...+…

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Q: 7. prove by mathematical induction that r(r+1) n+1 8. Prove by mathematical induction that 5"- 4n -…

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