Math 115 - Spring 1998 - Ribet - Midterm 2

# Math 115 - Spring 1998 - Ribet - Midterm 2 - 2 5(7 points...

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Math 115 Professor K. A. Ribet Last Midterm Exam April 8, 1998 The numbers 257 and 661 are prime. 1 (5 points) . Find the number of square roots of 9 modulo 3 · 11 2 · 13 3 . 2 (5 points) . Determine whether or not 116 is a square modulo 661. 3 (5 points) . Determine whether or not 116 is a cube modulo 661. 4 (5 points) . Calculate the number of primitive roots modulo 257
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Unformatted text preview: 2 . 5 (7 points) . Express-15 47 as a continued fraction. 6 (8 points) . Let p be a prime number dividing x 2 + 1, where x is an even integer. Show that p ≡ 1 mod 4 and that p is prime to x . Deduce that there are an inﬁnite number of primes congruent to 1 mod 4....
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