Unformatted text preview: H = [ a 4 ]. 4. Suppose K is a proper subgroup of H and H is a proper subgroup of G . ( H is a proper subgroup of G means that H is a subgroup but H 6 = G .) If j K j = 42 and j G j = 420, what are the possible orders of H . 5. Find the value of the Euler phifunction ` ( n ) for (a) n = 97; (b) n = 8800. 6. Use Euler’s Theorem (theorem 0.6.1) to ﬂnd a number a with 0 • a < 73 with a · 9 794 (mod 73) : 7. For each part, ﬂnd the smallest positive x that solves the given simultaneous congruences. (a) x · 5 (mod 7) and x · 5 (mod 9) (b) x · 5 (mod 5) and x · 2 (mod 12) and x · 8 (mod 13) Math 4023 1...
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This document was uploaded on 12/28/2011.
 Fall '09

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