Question

Euclidean algorithm:

Find integers a and b such that 70a+182b=28. Are the integers c and d such that 70c+182d=30?

show your work please.

Answer 1

We have to find integers a and b such that 70a+182b =28

If we take a=3 and b= -1 then it satisfies the given equation

Also 3 and -1 are integers

That is 70a+182b=28

70×3+182×(-1)

210-182=28 Hence proved

Hence answer is a=3 and b=-1

For second Question

We have to find integers c and d such that

70c+182d=30

We see that there is no integers c and d which satisfies 70a+182d=30

Hence in this case there is no any integers c and d which satisfies

70c+182d=30