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The Public Key
Age 16 to 18
Challenge Level 
This problem is intended to be tackled in conjunction with reading
the article on Public Key Cryptography though it is not essential
to understand the details of Public Key Cryptography in order to do
the problem. In itself it is a challenge to systematically reduce
the large number $180^{59}$ (using modulus arithmetic) to one which
the calculator can handle and finally to its equivalent modulo 391.
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