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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}`

.