Find the smallest positive integer k satisfying the stated condition or explain no such k exists: 2^k -= 1 mod 14.

BenoguigoliB 2021-01-04 Answered
Find the smallest positive integer k satisfying the stated condition or explain no such k exists:
2k1mod14.
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Expert Answer

Mitchel Aguirre
Answered 2021-01-05 Author has 94 answers

Find 2k(mod14) for some values of k.
212(mod14)
224(mod14)
238(mod14)
242(mod14)
254(mod14)
......
So, 2k(mod14) gives the value 2,4 or 8 for any positive integer k.
Hence, there exists no positive integer k such that 2k1(mod14).

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