am_lect_08 - Announcements Second HW due today Quiz 1 is on...

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Announcements Second HW due today Quiz 1 is on Wednesday, here, first 15 minutes of class http://www.cs.uiuc.edu/class/sp10/cs173
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Number Theory A branch of mathematics focused on integers Very important applications in: — Cryptography — Randomized algorithms and data-structures (e.g., hash tables) — Acoustics Definition : a Z divides b Z if n Z , b = a . n — Notation: a b a is a factor of b b is a multiple of a Examples : 7 77, because 77 = ( 11)( 7) and 11 Z 7 0, because 0 = 0 × 7 and 0 Z Does 0 7? Does 0 0?
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a , b , c Z , a b a c a ( b + c ) Proof : Suppose a , b and c are integers such that a b and a c Then, by definition, n Z , b = an and m Z , c = am Hence, b + c = ( an + am ) = a ( n + m ), where ( n + m ) Z Hence, a ( b + c ) Similarly: a , b , c Z , a b a bc
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am_lect_08 - Announcements Second HW due today Quiz 1 is on...

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