24. Determine whether each of these integers is prime, verifying some of Mersenne's claims a) 2 -1 c) 2" -I b) 2-1 d) 2-1

Q: Prove that if n is a +ive integer,

A: Given that, M xddxnf(x);p = (-1)npnF(p) We can prove this by mathematical induction.

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Q: 17. Prove that n is square - free every prime number to sat:sfies does not divide ).

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Q: b. Prove that the integer 359,240,758 cannot be a perfect quartic. (i.e. fourth power) The 758 ppose

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Q: 1. Prove that 5 is irrational.

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Q: Discrete

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Q: 24. Show that if p is a prime and k is an integer such that Isksp-1.then p divides ().

A: See the handwritten solution

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Q: of

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.