(c) For each integer a, if a 4 (mod 8), then a 2 (mod 8).

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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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10 c
(a) a +b =1 (mod 3);
(b) a b 1 (mod 3).
9. Let a and b be integers. Prove that if a =7 (mod 8) and b = 3 (mod 8),
then:
(a) a +b = 2 (mod 8);
(b) a · b = 5 (mod 8).
10. Determine if each of the following propositions is true or false. Justify each
conclusion.
(a) For all integers a and b, if ab = 0 (mod 6), then a = 0 (mod 6) or
b =0 (mod 6).
(b) For each integer a, if a = 2 (mod 8), then a=4 (mod 8).
(c) For each integer a, if a² = 4 (mod 8), then a = 2 (mod 8).
Transcribed Image Text:(a) a +b =1 (mod 3); (b) a b 1 (mod 3). 9. Let a and b be integers. Prove that if a =7 (mod 8) and b = 3 (mod 8), then: (a) a +b = 2 (mod 8); (b) a · b = 5 (mod 8). 10. Determine if each of the following propositions is true or false. Justify each conclusion. (a) For all integers a and b, if ab = 0 (mod 6), then a = 0 (mod 6) or b =0 (mod 6). (b) For each integer a, if a = 2 (mod 8), then a=4 (mod 8). (c) For each integer a, if a² = 4 (mod 8), then a = 2 (mod 8).
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