Congruences and probability
0
Suppose that $6x equiv 10y pmod{14}$. Which of the following are guaranteed to be true?
(a) $3x equiv 5y pmod{14}$: True
(b) $6x equiv 10y pmod{7}$: True
(c) $3x equiv 5y pmod{7}$: True
(d) $6x equiv 10y pmod{28}$: False
Am I right?
elementary-number-theory discrete-mathematics modular-arithmetic
edited Nov 28 '18 at 10:35
N. F. Taussig
43.6k93355
asked Nov 28 '18 at 3:09
Laura1999
202
add a comment |
0
Suppose that $6x equiv 10y pmod{14}$. Which of the following are guaranteed to be true?
(a) $3x equiv 5y pmod{14}$: True
(b) $6x equiv 10y pmod{7}$: True
(c) $3x equiv 5y pmod{7}$: True
(d) $6x equiv 10y pmod{28}$: False
Am I right?
elementary-number-theory discrete-mathematics modular-arithmetic
edited Nov 28 '18 at 10:35
N. F. Taussig
43.6k93355
asked Nov 28 '18 at 3:09
Laura1999
202
2
any reasoning for reaching the conclusion?
– Siong Thye Goh
Nov 28 '18 at 3:10
2
$b,c,d$ have correct answers. You need to check if $(a)$ is written correctly, because $3x-5y$ is half of $6x-10y$, so the latter being a multiple of $14$ would not imply that half of it is a multiple of $14$,right?
– астон вілла олоф мэллбэрг
Nov 28 '18 at 3:29
Please explain your reasoning rather than simply posting proposed answers. That might help you discover any errors you have made. It also helps us identify any errors you may have made. Also, please read this tutorial, which explains how to typeset mathematics on this site.
– N. F. Taussig
Nov 28 '18 at 10:37
note that $6cdot 7equiv 10cdot 0 pmod{14}$ does not imply $3cdot 7 equiv 5cdot 0 pmod{14}$, so $a)$ is false.
– farruhota
Nov 28 '18 at 14:14
Thank you for help!
– Laura1999
Nov 28 '18 at 23:27
add a comment |
0
0
0
Suppose that $6x equiv 10y pmod{14}$. Which of the following are guaranteed to be true?
(a) $3x equiv 5y pmod{14}$: True
(b) $6x equiv 10y pmod{7}$: True
(c) $3x equiv 5y pmod{7}$: True
(d) $6x equiv 10y pmod{28}$: False
Am I right?
elementary-number-theory discrete-mathematics modular-arithmetic
edited Nov 28 '18 at 10:35
N. F. Taussig
43.6k93355
asked Nov 28 '18 at 3:09
Laura1999
202
Suppose that $6x equiv 10y pmod{14}$. Which of the following are guaranteed to be true?
(a) $3x equiv 5y pmod{14}$: True
(b) $6x equiv 10y pmod{7}$: True
(c) $3x equiv 5y pmod{7}$: True
(d) $6x equiv 10y pmod{28}$: False
Am I right?
elementary-number-theory discrete-mathematics modular-arithmetic
elementary-number-theory discrete-mathematics modular-arithmetic
edited Nov 28 '18 at 10:35
N. F. Taussig
43.6k93355
asked Nov 28 '18 at 3:09
Laura1999
202
edited Nov 28 '18 at 10:35
N. F. Taussig
43.6k93355
asked Nov 28 '18 at 3:09
Laura1999
202
edited Nov 28 '18 at 10:35
N. F. Taussig
43.6k93355
edited Nov 28 '18 at 10:35
N. F. Taussig
43.6k93355
edited Nov 28 '18 at 10:35
N. F. Taussig
43.6k93355
43.6k93355
asked Nov 28 '18 at 3:09
Laura1999
202
asked Nov 28 '18 at 3:09
Laura1999
202
asked Nov 28 '18 at 3:09
Laura1999
202
202
2
any reasoning for reaching the conclusion?
– Siong Thye Goh
Nov 28 '18 at 3:10
2
$b,c,d$ have correct answers. You need to check if $(a)$ is written correctly, because $3x-5y$ is half of $6x-10y$, so the latter being a multiple of $14$ would not imply that half of it is a multiple of $14$,right?
– астон вілла олоф мэллбэрг
Nov 28 '18 at 3:29
Please explain your reasoning rather than simply posting proposed answers. That might help you discover any errors you have made. It also helps us identify any errors you may have made. Also, please read this tutorial, which explains how to typeset mathematics on this site.
– N. F. Taussig
Nov 28 '18 at 10:37
note that $6cdot 7equiv 10cdot 0 pmod{14}$ does not imply $3cdot 7 equiv 5cdot 0 pmod{14}$, so $a)$ is false.
– farruhota
Nov 28 '18 at 14:14
Thank you for help!
– Laura1999
Nov 28 '18 at 23:27
add a comment |
2
any reasoning for reaching the conclusion?
– Siong Thye Goh
Nov 28 '18 at 3:10
2
$b,c,d$ have correct answers. You need to check if $(a)$ is written correctly, because $3x-5y$ is half of $6x-10y$, so the latter being a multiple of $14$ would not imply that half of it is a multiple of $14$,right?
– астон вілла олоф мэллбэрг
Nov 28 '18 at 3:29
Please explain your reasoning rather than simply posting proposed answers. That might help you discover any errors you have made. It also helps us identify any errors you may have made. Also, please read this tutorial, which explains how to typeset mathematics on this site.
– N. F. Taussig
Nov 28 '18 at 10:37
note that $6cdot 7equiv 10cdot 0 pmod{14}$ does not imply $3cdot 7 equiv 5cdot 0 pmod{14}$, so $a)$ is false.
– farruhota
Nov 28 '18 at 14:14
Thank you for help!
– Laura1999
Nov 28 '18 at 23:27
2
2
any reasoning for reaching the conclusion?
– Siong Thye Goh
Nov 28 '18 at 3:10
any reasoning for reaching the conclusion?
– Siong Thye Goh
Nov 28 '18 at 3:10
2
2
$b,c,d$ have correct answers. You need to check if $(a)$ is written correctly, because $3x-5y$ is half of $6x-10y$, so the latter being a multiple of $14$ would not imply that half of it is a multiple of $14$,right?
– астон вілла олоф мэллбэрг
Nov 28 '18 at 3:29
$b,c,d$ have correct answers. You need to check if $(a)$ is written correctly, because $3x-5y$ is half of $6x-10y$, so the latter being a multiple of $14$ would not imply that half of it is a multiple of $14$,right?
– астон вілла олоф мэллбэрг
Nov 28 '18 at 3:29
Please explain your reasoning rather than simply posting proposed answers. That might help you discover any errors you have made. It also helps us identify any errors you may have made. Also, please read this tutorial, which explains how to typeset mathematics on this site.
– N. F. Taussig
Nov 28 '18 at 10:37
Please explain your reasoning rather than simply posting proposed answers. That might help you discover any errors you have made. It also helps us identify any errors you may have made. Also, please read this tutorial, which explains how to typeset mathematics on this site.
– N. F. Taussig
Nov 28 '18 at 10:37
note that $6cdot 7equiv 10cdot 0 pmod{14}$ does not imply $3cdot 7 equiv 5cdot 0 pmod{14}$, so $a)$ is false.
– farruhota
Nov 28 '18 at 14:14
note that $6cdot 7equiv 10cdot 0 pmod{14}$ does not imply $3cdot 7 equiv 5cdot 0 pmod{14}$, so $a)$ is false.
– farruhota
Nov 28 '18 at 14:14
Thank you for help!
– Laura1999
Nov 28 '18 at 23:27
Thank you for help!
– Laura1999
Nov 28 '18 at 23:27
add a comment |
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2
any reasoning for reaching the conclusion?
– Siong Thye Goh
Nov 28 '18 at 3:10
2
$b,c,d$ have correct answers. You need to check if $(a)$ is written correctly, because $3x-5y$ is half of $6x-10y$, so the latter being a multiple of $14$ would not imply that half of it is a multiple of $14$,right?
– астон вілла олоф мэллбэрг
Nov 28 '18 at 3:29
Please explain your reasoning rather than simply posting proposed answers. That might help you discover any errors you have made. It also helps us identify any errors you may have made. Also, please read this tutorial, which explains how to typeset mathematics on this site.
– N. F. Taussig
Nov 28 '18 at 10:37
note that $6cdot 7equiv 10cdot 0 pmod{14}$ does not imply $3cdot 7 equiv 5cdot 0 pmod{14}$, so $a)$ is false.
– farruhota
Nov 28 '18 at 14:14
Thank you for help!
– Laura1999
Nov 28 '18 at 23:27