monochromatic solution to $xy=z$
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Is it true that for any $k geq 2$, there is an integer $n=n(k)$ such that for any $k$-coloring of ${1,...,n},$ the equation $xy=z$ has a monochromatic solution?
combinatorics elementary-number-theory additive-combinatorics
asked Jan 9 at 20:06
KenKen
40828
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add a comment |
$begingroup$
Is it true that for any $k geq 2$, there is an integer $n=n(k)$ such that for any $k$-coloring of ${1,...,n},$ the equation $xy=z$ has a monochromatic solution?
combinatorics elementary-number-theory additive-combinatorics
asked Jan 9 at 20:06
KenKen
40828
$endgroup$
add a comment |
$begingroup$
Is it true that for any $k geq 2$, there is an integer $n=n(k)$ such that for any $k$-coloring of ${1,...,n},$ the equation $xy=z$ has a monochromatic solution?
combinatorics elementary-number-theory additive-combinatorics
asked Jan 9 at 20:06
KenKen
40828
$endgroup$
Is it true that for any $k geq 2$, there is an integer $n=n(k)$ such that for any $k$-coloring of ${1,...,n},$ the equation $xy=z$ has a monochromatic solution?
combinatorics elementary-number-theory additive-combinatorics
combinatorics elementary-number-theory additive-combinatorics
asked Jan 9 at 20:06
KenKen
40828
asked Jan 9 at 20:06
KenKen
40828
asked Jan 9 at 20:06
KenKen
40828
asked Jan 9 at 20:06
KenKen
40828
asked Jan 9 at 20:06
KenKen
40828
40828
add a comment |
add a comment |
1 Answer
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Some hints :
This is a simple modification of Schur's theorem via an exponential.
This document from EPFL on page 35 contains a proof of Schur's theorem which you can adapt to your problem.
answered Jan 9 at 20:22
P. QuintonP. Quinton
1,658213
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add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
Some hints :
This is a simple modification of Schur's theorem via an exponential.
This document from EPFL on page 35 contains a proof of Schur's theorem which you can adapt to your problem.
answered Jan 9 at 20:22
P. QuintonP. Quinton
1,658213
$endgroup$
add a comment |
$begingroup$
Some hints :
This is a simple modification of Schur's theorem via an exponential.
This document from EPFL on page 35 contains a proof of Schur's theorem which you can adapt to your problem.
answered Jan 9 at 20:22
P. QuintonP. Quinton
1,658213
$endgroup$
add a comment |
$begingroup$
Some hints :
This is a simple modification of Schur's theorem via an exponential.
This document from EPFL on page 35 contains a proof of Schur's theorem which you can adapt to your problem.
answered Jan 9 at 20:22
P. QuintonP. Quinton
1,658213
$endgroup$
Some hints :
This is a simple modification of Schur's theorem via an exponential.
This document from EPFL on page 35 contains a proof of Schur's theorem which you can adapt to your problem.
answered Jan 9 at 20:22
P. QuintonP. Quinton
1,658213
edited Jan 10 at 21:47
answered Jan 9 at 20:22
P. QuintonP. Quinton
1,658213
answered Jan 9 at 20:22
P. QuintonP. Quinton
1,658213
answered Jan 9 at 20:22
P. QuintonP. Quinton
1,658213
1,658213
add a comment |
add a comment |
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