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Unformatted text preview: 8 → 5 but 3 × 2 n = 5. 3. Calculate 45 401 mod 8, i.e. the remainder when 45 401 is divided by 8. ±irst way: 45 401 ≡ 5 401 (mod 8) ≡ 5 · (5 2 ) 200 (mod 8) ≡ 5 · 1 200 (mod 8) ≡ 5 (mod 8) Second way: GCD(45, 8 )= 1 and φ (8) = 4 (Euler function). Therefore 45 4 ≡ 1 (mod 8) and 45 401 ≡ 45 · (45 4 ) 100 (mod 8) ≡ 45 (mod 8) ≡ 5 (mod 8)...
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This note was uploaded on 03/21/2011 for the course CMPSC 40 taught by Professor Egiceoclu during the Fall '09 term at UCSB.
 Fall '09
 Egiceoclu

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