Divisibility Check in different Moduli
So I'm working on modular arithmetic and encountered the following problem:
Assume that $(a cdot b) mod m = c$ and that I know $c$. Can I still check for divisibility of $c$ by $a$? A quick example tells me that checking whether $c mod a = 0$ does not work:
$((29*200) mod 512) mod 29 = 23$
But is this check impossible if $m < a cdot b$ or is there a way to find out whether $a | c$? Maybe if $m$ and $n$ are primes?
Thanks!
elementary-number-theory modular-arithmetic
asked Nov 28 '18 at 19:58
Aares
62
add a comment |
So I'm working on modular arithmetic and encountered the following problem:
Assume that $(a cdot b) mod m = c$ and that I know $c$. Can I still check for divisibility of $c$ by $a$? A quick example tells me that checking whether $c mod a = 0$ does not work:
$((29*200) mod 512) mod 29 = 23$
But is this check impossible if $m < a cdot b$ or is there a way to find out whether $a | c$? Maybe if $m$ and $n$ are primes?
Thanks!
elementary-number-theory modular-arithmetic
asked Nov 28 '18 at 19:58
Aares
62
$acdot b pmod m$ or $pmod n$?
– Maged Saeed
Nov 28 '18 at 20:02
The question is not at all clear. Please give a concrete example.
– Bill Dubuque
Nov 28 '18 at 20:05
I edited the question, I hope it's clearer now.
– Aares
Nov 28 '18 at 20:13
You seek to solve $ axequiv cpmod{m} $ for which see this answer.
– Bill Dubuque
Dec 1 '18 at 16:30
add a comment |
So I'm working on modular arithmetic and encountered the following problem:
Assume that $(a cdot b) mod m = c$ and that I know $c$. Can I still check for divisibility of $c$ by $a$? A quick example tells me that checking whether $c mod a = 0$ does not work:
$((29*200) mod 512) mod 29 = 23$
But is this check impossible if $m < a cdot b$ or is there a way to find out whether $a | c$? Maybe if $m$ and $n$ are primes?
Thanks!
elementary-number-theory modular-arithmetic
asked Nov 28 '18 at 19:58
Aares
62
So I'm working on modular arithmetic and encountered the following problem:
Assume that $(a cdot b) mod m = c$ and that I know $c$. Can I still check for divisibility of $c$ by $a$? A quick example tells me that checking whether $c mod a = 0$ does not work:
$((29*200) mod 512) mod 29 = 23$
But is this check impossible if $m < a cdot b$ or is there a way to find out whether $a | c$? Maybe if $m$ and $n$ are primes?
Thanks!
elementary-number-theory modular-arithmetic
elementary-number-theory modular-arithmetic
asked Nov 28 '18 at 19:58
Aares
62
asked Nov 28 '18 at 19:58
Aares
62
edited Nov 28 '18 at 21:19
asked Nov 28 '18 at 19:58
Aares
62
asked Nov 28 '18 at 19:58
Aares
62
asked Nov 28 '18 at 19:58
Aares
62
62
$acdot b pmod m$ or $pmod n$?
– Maged Saeed
Nov 28 '18 at 20:02
The question is not at all clear. Please give a concrete example.
– Bill Dubuque
Nov 28 '18 at 20:05
I edited the question, I hope it's clearer now.
– Aares
Nov 28 '18 at 20:13
You seek to solve $ axequiv cpmod{m} $ for which see this answer.
– Bill Dubuque
Dec 1 '18 at 16:30
add a comment |
$acdot b pmod m$ or $pmod n$?
– Maged Saeed
Nov 28 '18 at 20:02
The question is not at all clear. Please give a concrete example.
– Bill Dubuque
Nov 28 '18 at 20:05
I edited the question, I hope it's clearer now.
– Aares
Nov 28 '18 at 20:13
You seek to solve $ axequiv cpmod{m} $ for which see this answer.
– Bill Dubuque
Dec 1 '18 at 16:30
$acdot b pmod m$ or $pmod n$?
– Maged Saeed
Nov 28 '18 at 20:02
$acdot b pmod m$ or $pmod n$?
– Maged Saeed
Nov 28 '18 at 20:02
The question is not at all clear. Please give a concrete example.
– Bill Dubuque
Nov 28 '18 at 20:05
The question is not at all clear. Please give a concrete example.
– Bill Dubuque
Nov 28 '18 at 20:05
I edited the question, I hope it's clearer now.
– Aares
Nov 28 '18 at 20:13
I edited the question, I hope it's clearer now.
– Aares
Nov 28 '18 at 20:13
You seek to solve $ axequiv cpmod{m} $ for which see this answer.
– Bill Dubuque
Dec 1 '18 at 16:30
You seek to solve $ axequiv cpmod{m} $ for which see this answer.
– Bill Dubuque
Dec 1 '18 at 16:30
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3017618%2fdivisibility-check-in-different-moduli%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3017618%2fdivisibility-check-in-different-moduli%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$acdot b pmod m$ or $pmod n$?
– Maged Saeed
Nov 28 '18 at 20:02
The question is not at all clear. Please give a concrete example.
– Bill Dubuque
Nov 28 '18 at 20:05
I edited the question, I hope it's clearer now.
– Aares
Nov 28 '18 at 20:13
You seek to solve $ axequiv cpmod{m} $ for which see this answer.
– Bill Dubuque
Dec 1 '18 at 16:30