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0

$begingroup$

Consider $p$ a prime and $(1+palpha)$ then clearly taking congruences mod $p^m$
$$
prod_i=0^p^m-1(1+palpha)=(1+palpha)^p^m equiv 1+(palpha)^p^m(equiv 1 ???)
$$
What we can say if we take more generally:

$$
prod_i=0^p^m-1(1+palpha_i)
$$ is $equiv 1$ mod $p^m$ ? ( $alpha_i$ in general for different $i$ are different integers)
thanks for clarifications!

modular-arithmetic arithmetic

share|cite|improve this question

edited Mar 13 at 5:28

Jyrki Lahtonen

110k13171385

asked Mar 12 at 11:29

andresandres

2439

$endgroup$

add a comment | 

0

$begingroup$

Consider $p$ a prime and $(1+palpha)$ then clearly taking congruences mod $p^m$
$$
prod_i=0^p^m-1(1+palpha)=(1+palpha)^p^m equiv 1+(palpha)^p^m(equiv 1 ???)
$$
What we can say if we take more generally:

$$
prod_i=0^p^m-1(1+palpha_i)
$$ is $equiv 1$ mod $p^m$ ? ( $alpha_i$ in general for different $i$ are different integers)
thanks for clarifications!

modular-arithmetic arithmetic

share|cite|improve this question

edited Mar 13 at 5:28

Jyrki Lahtonen

110k13171385

asked Mar 12 at 11:29

andresandres

2439

$endgroup$

add a comment | 

$begingroup$

Consider $p$ a prime and $(1+palpha)$ then clearly taking congruences mod $p^m$
$$
prod_i=0^p^m-1(1+palpha)=(1+palpha)^p^m equiv 1+(palpha)^p^m(equiv 1 ???)
$$
What we can say if we take more generally:

$$
prod_i=0^p^m-1(1+palpha_i)
$$ is $equiv 1$ mod $p^m$ ? ( $alpha_i$ in general for different $i$ are different integers)
thanks for clarifications!

modular-arithmetic arithmetic

share|cite|improve this question

edited Mar 13 at 5:28

Jyrki Lahtonen

110k13171385

asked Mar 12 at 11:29

andresandres

2439

$endgroup$

share|cite|improve this question

edited Mar 13 at 5:28

Jyrki Lahtonen

110k13171385

asked Mar 12 at 11:29

andresandres

2439

share|cite|improve this question

edited Mar 13 at 5:28

Jyrki Lahtonen

110k13171385

asked Mar 12 at 11:29

andresandres

2439

edited Mar 13 at 5:28

Jyrki Lahtonen

110k13171385

edited Mar 13 at 5:28

Jyrki Lahtonen

110k13171385

asked Mar 12 at 11:29

andresandres

2439

asked Mar 12 at 11:29

andresandres

2439