Prove that every number to a power greater than 1 can be written as $X^n+1 = Sigma_i=1^n(a_iX^i-b_iY^i)$ Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)How to find $a$ & $b$ that satisfy $10^n+1=sum_i=1^n(a_i10^i-b_i9^i)$?Does such a natural number exist, that it would be divisible by every other natural numberAny irrational number can be raised to a power so that the result is an integer numberProve that every odd prime number can be written as a difference of two squares.Prove that every non-prime natural number $ > 1$ can be written in the form of $n+(n+2)+(n+4)+…+(n+2m) = p$Which natural numbers can be represented as a sum of natural numbers raised to different powers?Prove, that every $p$ prime has a multiple, which is smaller than $fracp^44$, it can be written down as the sum of five integer's fourth power.Prove that any natural number can be written as the sum of $n$ different powers of two (starting from $2^0$) each one multiplied by either 0 or 1Proving that every odd non-prime number can be factorized with factors greater than 1.Is every positive integer greater than $2$ the sum of a prime and two squares?How many numbers (positive integers) smaller than $n$ can be written as a sum of two or more consecutive power of 2 integers?
Fit odd number of triplets in a measure?
An isoperimetric-type inequality inside a cube
Noise in Eigenvalues plot
What was the last profitable war?
How to achieve cat-like agility?
Flight departed from the gate 5 min before scheduled departure time. Refund options
The test team as an enemy of development? And how can this be avoided?
Adapting the Chinese Remainder Theorem (CRT) for integers to polynomials
How do you write "wild blueberries flavored"?
How do Java 8 default methods hеlp with lambdas?
Are there any irrational/transcendental numbers for which the distribution of decimal digits is not uniform?
newbie Q : How to read an output file in one command line
How many time has Arya actually used Needle?
Why do C and C++ allow the expression (int) + 4*5;
As a dual citizen, my US passport will expire one day after traveling to the US. Will this work?
How to make an animal which can only breed for a certain number of generations?
When does a function NOT have an antiderivative?
How can I prevent/balance waiting and turtling as a response to cooldown mechanics
Where and when has Thucydides been studied?
Does the main washing effect of soap come from foam?
Vertical ranges of Column Plots in 12
French equivalents of おしゃれは足元から (Every good outfit starts with the shoes)
Why not use the yoke to control yaw, as well as pitch and roll?
Found this skink in my tomato plant bucket. Is he trapped? Or could he leave if he wanted?
Prove that every number to a power greater than 1 can be written as $X^n+1 = Sigma_i=1^n(a_iX^i-b_iY^i)$
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)How to find $a$ & $b$ that satisfy $10^n+1=sum_i=1^n(a_i10^i-b_i9^i)$?Does such a natural number exist, that it would be divisible by every other natural numberAny irrational number can be raised to a power so that the result is an integer numberProve that every odd prime number can be written as a difference of two squares.Prove that every non-prime natural number $ > 1$ can be written in the form of $n+(n+2)+(n+4)+…+(n+2m) = p$Which natural numbers can be represented as a sum of natural numbers raised to different powers?Prove, that every $p$ prime has a multiple, which is smaller than $fracp^44$, it can be written down as the sum of five integer's fourth power.Prove that any natural number can be written as the sum of $n$ different powers of two (starting from $2^0$) each one multiplied by either 0 or 1Proving that every odd non-prime number can be factorized with factors greater than 1.Is every positive integer greater than $2$ the sum of a prime and two squares?How many numbers (positive integers) smaller than $n$ can be written as a sum of two or more consecutive power of 2 integers?
$begingroup$
Prove that every number to a power greater than 1 can be written as
$X^n+1 = Sigma_i=1^n(a_iX^i-b_iY^i)$
for all natural numbers $X,Y$ where $X>Y$.
Further, there exist integers $c,d,e,f$ that result in a unique solution when $a_i,b_i$ are restricted to the ranges $cleq a_ileq d$ and $e leq b_ileq f$.
This is more general than a specific question I asked previously.
number-theory exponentiation natural-numbers
asked Apr 2 at 15:21
RasputinRasputin
134
$endgroup$
add a comment |
$begingroup$
Prove that every number to a power greater than 1 can be written as
$X^n+1 = Sigma_i=1^n(a_iX^i-b_iY^i)$
for all natural numbers $X,Y$ where $X>Y$.
Further, there exist integers $c,d,e,f$ that result in a unique solution when $a_i,b_i$ are restricted to the ranges $cleq a_ileq d$ and $e leq b_ileq f$.
This is more general than a specific question I asked previously.
number-theory exponentiation natural-numbers
asked Apr 2 at 15:21
RasputinRasputin
134
$endgroup$
add a comment |
$begingroup$
Prove that every number to a power greater than 1 can be written as
$X^n+1 = Sigma_i=1^n(a_iX^i-b_iY^i)$
for all natural numbers $X,Y$ where $X>Y$.
Further, there exist integers $c,d,e,f$ that result in a unique solution when $a_i,b_i$ are restricted to the ranges $cleq a_ileq d$ and $e leq b_ileq f$.
This is more general than a specific question I asked previously.
number-theory exponentiation natural-numbers
asked Apr 2 at 15:21
RasputinRasputin
134
$endgroup$
Prove that every number to a power greater than 1 can be written as
$X^n+1 = Sigma_i=1^n(a_iX^i-b_iY^i)$
for all natural numbers $X,Y$ where $X>Y$.
Further, there exist integers $c,d,e,f$ that result in a unique solution when $a_i,b_i$ are restricted to the ranges $cleq a_ileq d$ and $e leq b_ileq f$.
This is more general than a specific question I asked previously.
number-theory exponentiation natural-numbers
number-theory exponentiation natural-numbers
asked Apr 2 at 15:21
RasputinRasputin
134
asked Apr 2 at 15:21
RasputinRasputin
134
edited Apr 2 at 17:50
Rasputin
asked Apr 2 at 15:21
RasputinRasputin
134
asked Apr 2 at 15:21
RasputinRasputin
134
asked Apr 2 at 15:21
RasputinRasputin
134
134
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
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%2f3171991%2fprove-that-every-number-to-a-power-greater-than-1-can-be-written-as-xn1%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%2f3171991%2fprove-that-every-number-to-a-power-greater-than-1-can-be-written-as-xn1%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
