Verify Modulo Arithmatic Equation: (47/14)=1 (mod 11)

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The discussion centers on verifying the equation (47/14) = 1 (mod 11). The initial attempt to solve it involves using the multiplicative inverse of 14 modulo 11, leading to the conclusion that (47/14) simplifies to 1 mod 11. However, participants highlight that 47/14 is not an integer, raising questions about the validity of the equation in modular arithmetic. It is suggested that the problem might actually be asking to demonstrate that 47 divided by 14 in modular arithmetic equals 1, rather than treating the fraction directly. The conversation emphasizes the importance of understanding modular arithmetic's application to integers.
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Homework Statement



Can somebody please veryify for me that (47/14) = 1 (mod 11)

Homework Equations





The Attempt at a Solution



What I did was:

(47/14)

=(14)^-1(47)

=(3^-1)(3)

=1 (mod 11)
 
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47/14 isn't an integer. How can it be equal to 1 mod 11? Can you state what the real problem is?
 
rad0786, is it possible that the problem was to show that 47, divided by 14 in "mod 11 arithmetic", is equal to 1? That would make more sense than "show that (the fraction) 47/11 is equal to 1 (mod 11)" since, as Dick implied, "mod" arithmetic only applies to integers.
 
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