show that 2^45=57 mod 91
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Originally Posted by mancillaj3 show that 2^45=57 mod 91 What have you tried so far? If it's the size of the numbers that is putting you off, notice that . So start by finding 2^45 mod 7 (same problem, but easier arithmetic). Then find 2^45 mod 13.
Since , you should find that , and similarly . Conversely (by the Chinese remainder theorem) if and , then .