Unformatted text preview: 8 â†’ 5 but 3 Ã— 2 n = 5. 3. Calculate 45 401 mod 8, i.e. the remainder when 45 401 is divided by 8. Â±irst way: 45 401 â‰¡ 5 401 (mod 8) â‰¡ 5 Â· (5 2 ) 200 (mod 8) â‰¡ 5 Â· 1 200 (mod 8) â‰¡ 5 (mod 8) Second way: GCD(45, 8 )= 1 and Ï† (8) = 4 (Euler function). Therefore 45 4 â‰¡ 1 (mod 8) and 45 401 â‰¡ 45 Â· (45 4 ) 100 (mod 8) â‰¡ 45 (mod 8) â‰¡ 5 (mod 8)...
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 Fall '09
 Egiceoclu
 Division, Remainder, Santa Barbara, Euler

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