solving congruence $a^{6p−6} equiv 1 pmod{9p}$
0
$begingroup$
Let $p$ be a positive prime number different from $3$ and $a$ be an integer not divisible neither by $3$ nor by $p$. Show that in this case $a^{6p−6} equiv 1 pmod{9p}$
modular-arithmetic
edited Dec 13 '18 at 17:17
rtybase
11.1k21533
asked Dec 13 '18 at 17:08
Y.xinY.xin
114
$endgroup$
add a comment |
0
$begingroup$
Let $p$ be a positive prime number different from $3$ and $a$ be an integer not divisible neither by $3$ nor by $p$. Show that in this case $a^{6p−6} equiv 1 pmod{9p}$
modular-arithmetic
edited Dec 13 '18 at 17:17
rtybase
11.1k21533
asked Dec 13 '18 at 17:08
Y.xinY.xin
114
$endgroup$
3
$begingroup$
Not a bad time to share your effort after math.stackexchange.com/questions/3038266/…
$endgroup$
– lab bhattacharjee
Dec 13 '18 at 17:10
$begingroup$
I have no idea about solving an equation. I need an example. If I know the first solution, I can do it in a similar way.
$endgroup$
– Y.xin
Dec 13 '18 at 17:16
4
$begingroup$
Apply Euler's theorem, since $varphi(9p)=varphi(9)cdot varphi(p)$
$endgroup$
– rtybase
Dec 13 '18 at 17:17
$begingroup$
I don't know what's the next steps. I get φ(9p)= 6⋅φ(p).
$endgroup$
– Y.xin
Dec 16 '18 at 18:09
add a comment |
0
0
0
$begingroup$
Let $p$ be a positive prime number different from $3$ and $a$ be an integer not divisible neither by $3$ nor by $p$. Show that in this case $a^{6p−6} equiv 1 pmod{9p}$
modular-arithmetic
edited Dec 13 '18 at 17:17
rtybase
11.1k21533
asked Dec 13 '18 at 17:08
Y.xinY.xin
114
$endgroup$
Let $p$ be a positive prime number different from $3$ and $a$ be an integer not divisible neither by $3$ nor by $p$. Show that in this case $a^{6p−6} equiv 1 pmod{9p}$
modular-arithmetic
modular-arithmetic
edited Dec 13 '18 at 17:17
rtybase
11.1k21533
asked Dec 13 '18 at 17:08
Y.xinY.xin
114
edited Dec 13 '18 at 17:17
rtybase
11.1k21533
asked Dec 13 '18 at 17:08
Y.xinY.xin
114
edited Dec 13 '18 at 17:17
rtybase
11.1k21533
edited Dec 13 '18 at 17:17
rtybase
11.1k21533
edited Dec 13 '18 at 17:17
rtybase
11.1k21533
11.1k21533
asked Dec 13 '18 at 17:08
Y.xinY.xin
114
asked Dec 13 '18 at 17:08
Y.xinY.xin
114
asked Dec 13 '18 at 17:08
Y.xinY.xin
114
114
3
$begingroup$
Not a bad time to share your effort after math.stackexchange.com/questions/3038266/…
$endgroup$
– lab bhattacharjee
Dec 13 '18 at 17:10
$begingroup$
I have no idea about solving an equation. I need an example. If I know the first solution, I can do it in a similar way.
$endgroup$
– Y.xin
Dec 13 '18 at 17:16
4
$begingroup$
Apply Euler's theorem, since $varphi(9p)=varphi(9)cdot varphi(p)$
$endgroup$
– rtybase
Dec 13 '18 at 17:17
$begingroup$
I don't know what's the next steps. I get φ(9p)= 6⋅φ(p).
$endgroup$
– Y.xin
Dec 16 '18 at 18:09
add a comment |
3
$begingroup$
Not a bad time to share your effort after math.stackexchange.com/questions/3038266/…
$endgroup$
– lab bhattacharjee
Dec 13 '18 at 17:10
$begingroup$
I have no idea about solving an equation. I need an example. If I know the first solution, I can do it in a similar way.
$endgroup$
– Y.xin
Dec 13 '18 at 17:16
4
$begingroup$
Apply Euler's theorem, since $varphi(9p)=varphi(9)cdot varphi(p)$
$endgroup$
– rtybase
Dec 13 '18 at 17:17
$begingroup$
I don't know what's the next steps. I get φ(9p)= 6⋅φ(p).
$endgroup$
– Y.xin
Dec 16 '18 at 18:09
3
3
$begingroup$
Not a bad time to share your effort after math.stackexchange.com/questions/3038266/…
$endgroup$
– lab bhattacharjee
Dec 13 '18 at 17:10
$begingroup$
Not a bad time to share your effort after math.stackexchange.com/questions/3038266/…
$endgroup$
– lab bhattacharjee
Dec 13 '18 at 17:10
$begingroup$
I have no idea about solving an equation. I need an example. If I know the first solution, I can do it in a similar way.
$endgroup$
– Y.xin
Dec 13 '18 at 17:16
$begingroup$
I have no idea about solving an equation. I need an example. If I know the first solution, I can do it in a similar way.
$endgroup$
– Y.xin
Dec 13 '18 at 17:16
4
4
$begingroup$
Apply Euler's theorem, since $varphi(9p)=varphi(9)cdot varphi(p)$
$endgroup$
– rtybase
Dec 13 '18 at 17:17
$begingroup$
Apply Euler's theorem, since $varphi(9p)=varphi(9)cdot varphi(p)$
$endgroup$
– rtybase
Dec 13 '18 at 17:17
$begingroup$
I don't know what's the next steps. I get φ(9p)= 6⋅φ(p).
$endgroup$
– Y.xin
Dec 16 '18 at 18:09
$begingroup$
I don't know what's the next steps. I get φ(9p)= 6⋅φ(p).
$endgroup$
– Y.xin
Dec 16 '18 at 18:09
add a comment |
0
active
oldest
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3
$begingroup$
Not a bad time to share your effort after math.stackexchange.com/questions/3038266/…
$endgroup$
– lab bhattacharjee
Dec 13 '18 at 17:10
$begingroup$
I have no idea about solving an equation. I need an example. If I know the first solution, I can do it in a similar way.
$endgroup$
– Y.xin
Dec 13 '18 at 17:16
4
$begingroup$
Apply Euler's theorem, since $varphi(9p)=varphi(9)cdot varphi(p)$
$endgroup$
– rtybase
Dec 13 '18 at 17:17
$begingroup$
I don't know what's the next steps. I get φ(9p)= 6⋅φ(p).
$endgroup$
– Y.xin
Dec 16 '18 at 18:09