# Chapter 4 - Section 4.1 - Divisibility and Modular Arithmetic - Exercises - Page 245: 32

a) 6 mod 369 b) 64 mod 2859 c) 441 mod 2116 d) 216 mod 74250

#### Work Step by Step

a) (361 mod 41) mod 9=(33 mod 41) mod 9= 6 mod 369 b) (32768 mod 13)$^2$ mod 11 =(8 mod 13)$^2$ mod 11 =64 mod 2859 c) (49*7 mod 23)$^2$ mod 31 = (21 mod 23)$^2$ mod 31 =(441 mod 529) mod 31 =441 mod 2116 d) (216 mod 3375) mod 22 = 216 mod 74250

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