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Formally, a number n, has an inverse mod p only if p is prime. The inverse of n, mod p, is one of the numbers {0, 1, 2, ... , k-1} such that n*(p-1) = 1 mod p
If p is not a prime then:
if n is a factor of p then there is no such "inverse"; and
if n is not a factor of p then there may be several possible "inverses".
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Find the inverse of 4 mod 17?
is it 4 inverse of mod 17 or whole inverse? Whole inverse do not make sence, so, ans for the q is 13.
How do you find pairs of numbers which are equal?
Numbers. i^n = i^(n mod 4). With n = 27, 27 mod 4...
Additive inverse property?
Additive inverse just means that when you add them, it equals 0. So, 1 and -1; 12 and -12; -74 and 74; 0 and -0. It can also be applied to things other than integers: x+12 and -x-12; 2x-3 and -2x+3 (which is the same as 3-2x) Or, if you know anything about modular arithmetic, then: 7+x≡0 (mod 9) and 2; 6-x≡4 (mod 7) and -2
How do you find inverse of matrix in hill cipher technique?
You must study the Linear congruence theorem and the extended GCD algorithm, which belong to Number Theory, in order to understand the maths behind modulo arithmetic.The inverse of matrix K for example is (1/det(K)) * adjoint(K), where det(K) 0.I assume that you don't understand how to calculate the 1/det(K) in modulo arithmetic and here is where linear congruences and GCD come to play.Your K has det(K) = -121. Lets say that the modulo m is 26. We want x*(-121) = 1 (mod 26).[ a = b (mod m) means that a-b = N*m]We can easily find that for x=3 the above congruence is true because 26 divides (3*(-121) -1) exactly. Of course, the correct way is to use GCD in reverse to calculate the x, but I don't have time for explaining how do it. Check the extented GCD algorithm :)Now, inv(K) = 3*([3 -8], [-17 5]) (mod 26) = ([9 -24], [-51 15]) (mod 26) = ([9 2], [1 15]).
What is meant by modulus of any number?
One number "modulo" another number indicates the remainder after division of the first number by the second. For example, the integer result of 11 / 2 is 5 with a remainder of 1, so 11 mod 2 = 1. (In fact, any odd number mod 2 = 1.)
