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Homework answers / question archive / For Fermat's Primality test, and only for Fermat, mod exponentiatron can be done on Wolframalpha

For Fermat's Primality test, and only for Fermat, mod exponentiatron can be done on Wolframalpha.com using the PowerMod command. For example, Power Mod[12, 34, 56] computes 1234 mod 56 1 Consider the integer n = 527. (a) Show it is not prime by using the primality testing method from Week 4. (b) Use Fermat's Primality Test to show that n = 527 is not prime. You can use Wolfra- malpha.com or similar software to do the modular exponentiatron for you. (c) In (la) you found a factor of 527. What is the prime factorization? Use Fermat's Little Theorem to find a value of x such that 12% = 1 mod 527 (d) Use fast modular exponentiatron to confirm that this is true. (e) Use Fermat's Little Theorem, as stated above, to find 122402 mod 527 (f) Why can't Fermat's Little Theorem be used to find the following?