(a) Explanation Proof: Let us we know that D n is given by, D n = n ! ( 1 − 1 1 ! + 1 2 ! + 1 3 ! − ..... + ( − 1 ) n 1 n ! ) Now we can write that, D n = n ! ( 1 − 1 1 ! + 1 2 ! + 1 3 ! − ..... + ( − 1 ) n 1 n ! ) = ( n ! − n ! + n ( n − 1 ) ( n − 2 ) ....3 ⋅ 2 ! 2 ! − n ( n − 1 ) ( n − 2 ) ....4.3 ! 3 ! ) = n ( n − 1 ) ( n − 2 ) .......3 − n ( n − 1 ) ( n − 2 ) (b) To determine To Prove: The D n is even if and only if n is odd.

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ISBN: 9780131679955

Author: Edgar G. Goodaire

Publisher: Prentice Hall

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Chapter 7.6, Problem 10E

(a)

To determine

To Prove: The DN≡(−1)n(mod n).

(b)

To determine

To Prove: The Dn is even if and only if n is odd.

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Chapter 7.6, Problem 9E

Chapter 7.6, Problem 11E

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Chapter 7 Solutions

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To Prove: The D N ≡ ( − 1 ) n ( mod n ) .

Solution Summary: The author explains that D_n is given by, Beginarrayl=(n-1)

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To Prove: The DN≡(−1)n(mod n).

To Prove: The Dn is even if and only if n is odd.

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