Question

29. a) Use Fermat's Little Theorem to compute 5 2003 mod 7,

29. a) Use Fermat's Little Theorem to compute 5 2003 mod 7,
5 2003 mod 11, and 5 2003 mod 13.
b) Use your results from part (a) and the Chinese Re-
mainder Theorem to find 5 2003 mod 1001. (Note that
1 00 1 = 7 . 11 . 13.)
IGr Let n be a positive integer and let n – 1 = 2 S t, where s is a
nonnegative integer and t is an odd positive integer. We say
that n passes Miller's test for the base b if either b t = 1 (mod
n) or b 2Jt = -1 (mod n) for some j with 0 < j < s – 1. It
can be shown (see [Ro05]) that a composite integer n passes
Miller's test for fewer than n/4 bases b with 1 < b < n.

from discrete math and its appl.

chap 3.7 # 29

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