Unformatted text preview: over. How many troops survived the battle? 4: (a) Find φ ( n ) for all integers n with 20 ≤ n ≤ 30. (b) Find all positive integers n such that φ ( n ) = 60. 5: (a) Show that 2 340 ≡ 1 (mod 341). (b) Show that 21 ± ± (4 n 7 + 7 n 3 + 10 n ) for all integers n . (c) Find a positive integer k such that the number 3 k ends with the digits 0001. (d) Let n = p k for some positive integer k where p is prime with p ≡ 3 (mod 4). Show that the congruence x 2 ≡ 1 (mod n ) has no solution....
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 Spring '08
 ANDREWCHILDS
 Algebra, Congruence, Natural number, Prime number

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