Unformatted text preview: n with n â‰¡ 1 mod 100 and n â‰¡ 4 mod 1000. Solution. False. (vii) There is an integer n with n â‰¡ 1 mod 100 and n â‰¡ 4 mod 1001. Solution. True. (viii) If p is a prime and m â‰¡ n mod p , then a m â‰¡ a n mod p for every natural number a . Solution. False. 1.78 Find all the integers x which are solutions to each of the following congru-ences: (i) 3 x â‰¡ 2 mod 5. Solution. x â‰¡ 4 mod 5. (ii) 7 x â‰¡ 4 mod 10. Solution. x â‰¡ 12 mod 10....
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- Fall '11
- Remainder, Natural number, Prime number, Euclidean algorithm, Euclidean domain