Paper 4, Section I, E

Numbers and Sets | Part IA, 2015

(a) Find all integers xx and yy such that

6x+2y3(mod53) and 17x+4y7(mod53)6 x+2 y \equiv 3 \quad(\bmod 53) \quad \text { and } \quad 17 x+4 y \equiv 7 \quad(\bmod 53)

(b) Show that if an integer n>4n>4 is composite then (n1)!0(modn)(n-1) ! \equiv 0(\bmod n).

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