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The inverse of a modulo 39 is b. What is the inverse of 14a modulo 39 in terms of b? Give your answer as an expression in terms of b.

 May 26, 2021
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The inverse of a modulo 39 is b. What is the inverse of 14a modulo 39 in terms of b? Give your answer as an expression in terms of b.

 

I did this a really super long way using the Euclidean algorithm and got 

14a*14b=1 mod39

so the inverse of 14a is 14b  (mod39)

 

Maybe there is an easier way.  In this case trial and error would have been easier......

 

It is correct though   14a*14b= 196ab = 1*1 (mod39) = 1  (mod39)

 

Probably the fact that 39=3*13 should have been used, but I am not sure exactly how.  (I have never studied modulo arithmetic formally)

 May 26, 2021

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