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6 Nov 2019
Let a, b E Z and c, d E N. Prove or disprove each of the following statements. (a) If c | d and ax + by-c has a positive integer solution, then az + by d also has a positive integer solution (b) If gcd (a, b) = 1, d > c and az + by = c has a positive integer solution, then ax + by d also has a positive integer solution (A positive integer solution to the equation ax + by = c is a pair (zi, yi) N Ã N such that at1 ax +by- c.) Show transcribed image text
Let a, b E Z and c, d E N. Prove or disprove each of the following statements. (a) If c | d and ax + by-c has a positive integer solution, then az + by d also has a positive integer solution (b) If gcd (a, b) = 1, d > c and az + by = c has a positive integer solution, then ax + by d also has a positive integer solution (A positive integer solution to the equation ax + by = c is a pair (zi, yi) N Ã N such that at1 ax +by- c.)
Show transcribed image text Jean KeelingLv2
6 Nov 2019