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

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In summary, modulo arithmetic is a mathematical operation used to find the remainder after dividing one number by another. It is commonly used in computer science and encryption algorithms. To verify a modulo arithmetic equation, the operation must be performed and the remainder must match the specified value. The notation "a (mod n)" represents the remainder after dividing a by n. An example of a modulo arithmetic equation is (23/5)=3 (mod 7). Modulo arithmetic has various real-life applications, including cryptography, computer programming, data validation, and timekeeping.
  • #1
rad0786
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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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  • #2
47/14 isn't an integer. How can it be equal to 1 mod 11? Can you state what the real problem is?
 
  • #3
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.
 

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

What is Modulo Arithmatic?

Modulo Arithmatic is a mathematical operation that involves finding the remainder after division. It is denoted by the symbol "%". For example, 10%3 = 1, as the remainder after dividing 10 by 3 is 1.

What does (47/14)=1 (mod 11) mean?

This equation means that when 47 is divided by 14, the remainder is 1 when divided by 11. In other words, 47 divided by 14 leaves a remainder of 1 when divided by 11.

How do you verify a Modulo Arithmatic equation?

To verify a Modulo Arithmatic equation, you must perform the division and check if the remainder is equal to the number on the right side of the equation. In this case, we would divide 47 by 14 and check if the remainder is 1 when divided by 11.

What happens if the remainder is not equal to the number on the right side of the equation?

If the remainder is not equal, then the equation is not true. In Modulo Arithmatic, the remainder must be equal to the number on the right side of the equation for it to be considered correct.

Can Modulo Arithmatic be applied to all numbers?

Yes, Modulo Arithmatic can be applied to all numbers. However, it is most commonly used with integers and in computer science to perform calculations on large numbers.

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