Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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3. For n e N, we define n! = (n)(n – 1)(n – 2).. (2)(1). E.g., 4!
Prove the following statements.
(4)(3)(2)(1) = 24.
(a) Let a, b, c E N. If a|b and alc, then a|(b + c).
(b) Let n > 2 be a natural number. Use part (a) to prove that the numbers n! +
2, n! + 3, ..., and n! +n are all composite.
1
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Transcribed Image Text:3. For n e N, we define n! = (n)(n – 1)(n – 2).. (2)(1). E.g., 4! Prove the following statements. (4)(3)(2)(1) = 24. (a) Let a, b, c E N. If a|b and alc, then a|(b + c). (b) Let n > 2 be a natural number. Use part (a) to prove that the numbers n! + 2, n! + 3, ..., and n! +n are all composite. 1
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