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.
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
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