Math 3221 Number Theory - Homework Until Test 2 Worksheet With Answers - Philipp Braun Page 9
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16+1
1
7. For n
1, show that ( 13)
( 13) + ( 13)
(mod 181).
2
1
Proof. For n = 1, the statement is true because ( 13)
169
12
13
+
0
(k+1)+1
( 13)
(mod 181). Assume the statement is true for n = k. Then ( 13)
k
k 1
k+1
(k+1) 1
( 13) ( 13)
+ ( 13)
( 13)
+ ( 13)
(mod 181).
9
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