MAS 4203 Final: numthy-sp02-final

• School: University of Florida
• Department: Mathematics-Algebraic Structure
• Course: MAS 4203
• Professor: All

Document Summary

Let a, b, c z with (a, b) = 1. 1. assuming the fundamental theorem of arithmetic) that if a | c and. Hint: since (a, b) = 1 there are integers x, y such that ax + by = 1. 2. zero and let d = (a, b). Let a, b, c z and assume that a and b are not both ax + by = c for some integers x and y if and only if d | c. Hint: use the result that (a, b) = min{ma + nb : m, n z, ma + nb > 0}. [5 + 15 = 20 points] (i) de ne pseudoprime. (ii) prove that 161038 = (2)(73)(1103) is a pseudoprime. [5 + 15 = 20 points] (i) state euler"s theorem. (ii) let m, n be positive relatively prime integers. Prove that m (n) + n (m) 1 (mod mn). Prove that h(n) = f (n)g(n) is multiplicative.