N has all divisors up to 31 except two The Next CEO of Stack OverflowNumber theory problem divides“Quadly” numbers with just 4 factorsTrue or false division algorithm problemProve that $1$ has only one divisorA Question Related to Zsigmondy's Theoremnumber system and divisibilityWritten as sum of positive divisorsUnder what conditions does an integer dividing the square of n imply that the integer must divide n?divisibility proofProve that if $3n^2 + 2n$ is even, then $n$ is even
Is there an equivalent of cd - for cp or mv
Purpose of level-shifter with same in and out voltages
How do you define an element with an ID attribute using LWC?
How to Implement Deterministic Encryption Safely in .NET
What CSS properties can the br tag have?
Would a grinding machine be a simple and workable propulsion system for an interplanetary spacecraft?
Free fall ellipse or parabola?
Aggressive Under-Indexing and no data for missing index
Man transported from Alternate World into ours by a Neutrino Detector
How to avoid supervisors with prejudiced views?
What flight has the highest ratio of timezone difference to flight time?
Reshaping json / reparing json inside shell script (remove trailing comma)
Is it okay to majorly distort historical facts while writing a fiction story?
Getting Stale Gas Out of a Gas Tank w/out Dropping the Tank
In the "Harry Potter and the Order of the Phoenix" video game, what potion is used to sabotage Umbridge's speakers?
What is the process for purifying your home if you believe it may have been previously used for pagan worship?
Why do we say 'Un seul M' and not 'Une seule M' even though M is a "consonne"
Won the lottery - how do I keep the money?
Cannot shrink btrfs filesystem although there is still data and metadata space left : ERROR: unable to resize '/home': No space left on device
Is Nisuin Biblical or Rabbinic?
Could a dragon use its wings to swim?
Airplane gently rocking its wings during whole flight
Help/tips for a first time writer?
Which one is the true statement?
N has all divisors up to 31 except two
The Next CEO of Stack OverflowNumber theory problem divides“Quadly” numbers with just 4 factorsTrue or false division algorithm problemProve that $1$ has only one divisorA Question Related to Zsigmondy's Theoremnumber system and divisibilityWritten as sum of positive divisorsUnder what conditions does an integer dividing the square of n imply that the integer must divide n?divisibility proofProve that if $3n^2 + 2n$ is even, then $n$ is even
$begingroup$
Let $N$ be a positive integer. It is true that $1|N, 2|N, 3|N, dots, 31|N$, except two. Which are false?
It seems like the problem is impossible. For example, any two consecutive integers must have an even integer E, and this even integer is divisible by 2 and an integer less than it, and since 2 and that integer divide N, E must divide $N$, which is a contradiction. For example, if we chose 31 and 30, then since 2 and 15 divide N, it must be the case that 30 divides $N$, which is a contradiction. So I'm not sure where to go with this problem.
divisibility
asked Mar 19 at 21:28
WesleyWesley
609413
$endgroup$
add a comment |
$begingroup$
Let $N$ be a positive integer. It is true that $1|N, 2|N, 3|N, dots, 31|N$, except two. Which are false?
It seems like the problem is impossible. For example, any two consecutive integers must have an even integer E, and this even integer is divisible by 2 and an integer less than it, and since 2 and that integer divide N, E must divide $N$, which is a contradiction. For example, if we chose 31 and 30, then since 2 and 15 divide N, it must be the case that 30 divides $N$, which is a contradiction. So I'm not sure where to go with this problem.
divisibility
asked Mar 19 at 21:28
WesleyWesley
609413
$endgroup$
$begingroup$
I understand the problem as follows: Of the 31 statements $i|N, i=1,2,ldots,31$ 29 are true and 2 are false. Which are the 2 that are false? As your example shows, an even divisor is likely not among them.
$endgroup$
– Ingix
Mar 19 at 21:42
$begingroup$
It seems like there is more than one solution. We could have $$N= 31!over 17cdot19$$ but we could choose any two primes $17leq p,qleq31$ in the denominator.
$endgroup$
– saulspatz
Mar 19 at 22:10
add a comment |
$begingroup$
Let $N$ be a positive integer. It is true that $1|N, 2|N, 3|N, dots, 31|N$, except two. Which are false?
It seems like the problem is impossible. For example, any two consecutive integers must have an even integer E, and this even integer is divisible by 2 and an integer less than it, and since 2 and that integer divide N, E must divide $N$, which is a contradiction. For example, if we chose 31 and 30, then since 2 and 15 divide N, it must be the case that 30 divides $N$, which is a contradiction. So I'm not sure where to go with this problem.
divisibility
asked Mar 19 at 21:28
WesleyWesley
609413
$endgroup$
Let $N$ be a positive integer. It is true that $1|N, 2|N, 3|N, dots, 31|N$, except two. Which are false?
It seems like the problem is impossible. For example, any two consecutive integers must have an even integer E, and this even integer is divisible by 2 and an integer less than it, and since 2 and that integer divide N, E must divide $N$, which is a contradiction. For example, if we chose 31 and 30, then since 2 and 15 divide N, it must be the case that 30 divides $N$, which is a contradiction. So I'm not sure where to go with this problem.
divisibility
divisibility
asked Mar 19 at 21:28
WesleyWesley
609413
asked Mar 19 at 21:28
WesleyWesley
609413
asked Mar 19 at 21:28
WesleyWesley
609413
asked Mar 19 at 21:28
WesleyWesley
609413
asked Mar 19 at 21:28
WesleyWesley
609413
609413
$begingroup$
I understand the problem as follows: Of the 31 statements $i|N, i=1,2,ldots,31$ 29 are true and 2 are false. Which are the 2 that are false? As your example shows, an even divisor is likely not among them.
$endgroup$
– Ingix
Mar 19 at 21:42
$begingroup$
It seems like there is more than one solution. We could have $$N= 31!over 17cdot19$$ but we could choose any two primes $17leq p,qleq31$ in the denominator.
$endgroup$
– saulspatz
Mar 19 at 22:10
add a comment |
$begingroup$
I understand the problem as follows: Of the 31 statements $i|N, i=1,2,ldots,31$ 29 are true and 2 are false. Which are the 2 that are false? As your example shows, an even divisor is likely not among them.
$endgroup$
– Ingix
Mar 19 at 21:42
$begingroup$
It seems like there is more than one solution. We could have $$N= 31!over 17cdot19$$ but we could choose any two primes $17leq p,qleq31$ in the denominator.
$endgroup$
– saulspatz
Mar 19 at 22:10
$begingroup$
I understand the problem as follows: Of the 31 statements $i|N, i=1,2,ldots,31$ 29 are true and 2 are false. Which are the 2 that are false? As your example shows, an even divisor is likely not among them.
$endgroup$
– Ingix
Mar 19 at 21:42
$begingroup$
I understand the problem as follows: Of the 31 statements $i|N, i=1,2,ldots,31$ 29 are true and 2 are false. Which are the 2 that are false? As your example shows, an even divisor is likely not among them.
$endgroup$
– Ingix
Mar 19 at 21:42
$begingroup$
It seems like there is more than one solution. We could have $$N= 31!over 17cdot19$$ but we could choose any two primes $17leq p,qleq31$ in the denominator.
$endgroup$
– saulspatz
Mar 19 at 22:10
$begingroup$
It seems like there is more than one solution. We could have $$N= 31!over 17cdot19$$ but we could choose any two primes $17leq p,qleq31$ in the denominator.
$endgroup$
– saulspatz
Mar 19 at 22:10
add a comment |
0
active
oldest
votes
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%2f3154637%2fn-has-all-divisors-up-to-31-except-two%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.
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%2f3154637%2fn-has-all-divisors-up-to-31-except-two%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
$begingroup$
I understand the problem as follows: Of the 31 statements $i|N, i=1,2,ldots,31$ 29 are true and 2 are false. Which are the 2 that are false? As your example shows, an even divisor is likely not among them.
$endgroup$
– Ingix
Mar 19 at 21:42
$begingroup$
It seems like there is more than one solution. We could have $$N= 31!over 17cdot19$$ but we could choose any two primes $17leq p,qleq31$ in the denominator.
$endgroup$
– saulspatz
Mar 19 at 22:10