171sp07_homework12 - “I am not sure but it was certainly...

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550.171 Discrete Mathematics Spring 2007 Homework Assignment #12 will not be collected From the text: Section 35 / 35.13 Section 36 / 36.11, 36.12, 36.13 Section 37 / 37.1, 37.3 (b,d only) 12.1. Consider the following system of congruences: 11 x 4 (mod 14) 2 x 9 (mod 19) Find all integers x that satisfy both congruences simultaneously. Please do this problem without the use of a calculator first, then fell free to corroborate your results with a calculator. 12.2. I was asked by the dean “how many students were in statistics class today?” I responded,
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Unformatted text preview: “I am not sure, but it was certainly under 54.” I noticed that the dean did not look particularly pleased with my answer so I followed up with “But I also know that when I broke the class into groups of 7 there was 1 student left over; and when I broke them up into groups of 8 there was 2 left over.” Help me out by (rigorously) determining the number of students in my statistics class today....
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