Q2. (8 pts, Solving Congruences) Let a,b,d, and n1 be arbitrary integers. 2.a. Prove that if ad-=bd(modn), then a-=b(mod(n)/(gcd(d,n))). 2.b. Solve 7x-=12(mod13) for xin{0,1,2,dots,12}. 2.c. Solve 84x-38-=79(mod15) for xin{0,1,2,dots,14}. 2.d. Solve 2x-=3(mod14) for xin{0,1,2,dots,13}. solutionspile.com

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Q2. (8 pts, Solving Congruences) Let a,b,d, and n>1 be arbitrary integers. 2.a. Prove that if ad-=bd(modn), then a-=b(mod(n)/(gcd(d,n))). 2.b. Solve 7x-=12(mod13) for xin{0,1,2,dots,12}. 2.c. Solve 84x-38-=79(mod15) for xin{0,1,2,dots,14}. 2.d. Solve 2x-=3(mod14) for xin{0,1,2,dots,13}.  solutionspile.com

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