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The numbers 7 and 23 are relatively prime and therefore there must exist integers a andb ,such that 7a+23b=1 . a) Find such a pair

The numbers 7 and 23 are relatively prime and therefore there must exist integers a andb ,such that 7a+23b=1 .

a) Find such a pair of integers (a ,b)with the smallest possible a>0.

b) Determine the inverse of 7 in Z23 .

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