Hint Use the Euclidean AlgorithmSolution1 An element in I is

Hint: Use the Euclidean Algorithm

Solution

1)

An element in I is:35x+119y where x ,y are integers.

35x+199y=7*5x+7*17y=7(5x+17y)

5*7=35=17*2+1

So, 5*7-17*2=1

So, x=7, y=-2

7 is an element in I. And since 35 and 119 are multiples of 7 implies all elements are multiples of 7. Hence, I=(7)

2)

7=35*7-119*2

35*7=245

119*2=238

So, 35*7-199*2=7