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11.8.11  Inverse in ℤ/p

The inv or inverse command finds the inverse of an integer in ℤ/pℤ.

Since ℤ/pℤ is only a field if p is prime, the inverse is only guaranteed to exist if p is prime (and the integer is non-zero).

Example

inv(3%13)
     

−4
%13
          

Indeed, 3·(−4)=−12≡ 1(mod 13 ).

You can also find the reciprocal using division:

1/(3%13)
     

−4
%13
          

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