Problem of the day

  1. Secret message =
    "Y,B>j0r-B\xca?x3A+Yb\xc4& m".
    f(x) = ax mod N, a = 19, N = 1,000,000, block size = 3. What is the message?

  2. Is the number N1 =

    18811277023211276170
    87679512659599640999
    58352014316332881290
    46662122067416818277
    286993

    prime or composite? Why?

  3. Find the continued fraction expansion of the square roots of 2, 3, 5, 6, ... . What patterns do you see? Compute convergents of these continued fractions. How do they relate to solutions of Pell's equation?

  4. Find a prime number larger than 10100. Find the next five primes. How sure are you of your results?

  5. I have encoded my PIN using the function f(x) = x3 mod 12347. The result is 6803. What is my PIN?