Context
Please be advised, that the nature of the task is number theoretical, but the context should be interpreted as a probability problem! Currently I'm working on a project about hashing algorithms, and I have to formalize simple statements about a well specified, abstract system.
Objects
Set(S).: A finite set of "x" values (0; 16^64-1; and all the integers between them).
Operation.: Chosing an element then executing a mod9 operation.
Statements
1. Let's assume that with a random number function h(x), we can generate any k; where 0 ≤ k ≤ 16^64-1.
2. In any h(x) --> k mod 9, every value have an equal probability of taking 0-8 values.
Formalized nomenclature
Is there any way of writing the statements (in the context of the set and operation) above in a more elegant way? Is there any way of proving statement 2) --> using sequences or a general formula? e.g. n(mod9) n1(mod9) ... nk(mod9)?
This is only the half of the problem. After clarifcation, I would like to make the problem a little nuanced.
Thank you!
Please be advised, that the nature of the task is number theoretical, but the context should be interpreted as a probability problem! Currently I'm working on a project about hashing algorithms, and I have to formalize simple statements about a well specified, abstract system.
Objects
Set(S).: A finite set of "x" values (0; 16^64-1; and all the integers between them).
Operation.: Chosing an element then executing a mod9 operation.
Statements
1. Let's assume that with a random number function h(x), we can generate any k; where 0 ≤ k ≤ 16^64-1.
2. In any h(x) --> k mod 9, every value have an equal probability of taking 0-8 values.
Formalized nomenclature
Is there any way of writing the statements (in the context of the set and operation) above in a more elegant way? Is there any way of proving statement 2) --> using sequences or a general formula? e.g. n(mod9) n1(mod9) ... nk(mod9)?
This is only the half of the problem. After clarifcation, I would like to make the problem a little nuanced.
Thank you!
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