Explanation of the Wolstenholme theorem proof
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I recently came accross the Wolstenholme theorem which says that $$binom{ap}{bp} equiv binom{a}{b} pmod {p^{3}}$$
On wikipedia, it gives a combinatorial proof of this theorem that involves splitting a set A of size ap into a rings of size p, but I don't understand the rest of the proof. Can someone help breakdown the group theory in that proof? I'm familiar with what a direct sum and what the cyclic group is, but I don't understand this proof.
number-theory binomial-coefficients proof-explanation
asked Dec 8 '18 at 22:16
Garage SensorGarage Sensor
334
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$begingroup$
I recently came accross the Wolstenholme theorem which says that $$binom{ap}{bp} equiv binom{a}{b} pmod {p^{3}}$$
On wikipedia, it gives a combinatorial proof of this theorem that involves splitting a set A of size ap into a rings of size p, but I don't understand the rest of the proof. Can someone help breakdown the group theory in that proof? I'm familiar with what a direct sum and what the cyclic group is, but I don't understand this proof.
number-theory binomial-coefficients proof-explanation
asked Dec 8 '18 at 22:16
Garage SensorGarage Sensor
334
$endgroup$
add a comment |
$begingroup$
I recently came accross the Wolstenholme theorem which says that $$binom{ap}{bp} equiv binom{a}{b} pmod {p^{3}}$$
On wikipedia, it gives a combinatorial proof of this theorem that involves splitting a set A of size ap into a rings of size p, but I don't understand the rest of the proof. Can someone help breakdown the group theory in that proof? I'm familiar with what a direct sum and what the cyclic group is, but I don't understand this proof.
number-theory binomial-coefficients proof-explanation
asked Dec 8 '18 at 22:16
Garage SensorGarage Sensor
334
$endgroup$
I recently came accross the Wolstenholme theorem which says that $$binom{ap}{bp} equiv binom{a}{b} pmod {p^{3}}$$
On wikipedia, it gives a combinatorial proof of this theorem that involves splitting a set A of size ap into a rings of size p, but I don't understand the rest of the proof. Can someone help breakdown the group theory in that proof? I'm familiar with what a direct sum and what the cyclic group is, but I don't understand this proof.
number-theory binomial-coefficients proof-explanation
number-theory binomial-coefficients proof-explanation
asked Dec 8 '18 at 22:16
Garage SensorGarage Sensor
334
asked Dec 8 '18 at 22:16
Garage SensorGarage Sensor
334
asked Dec 8 '18 at 22:16
Garage SensorGarage Sensor
334
asked Dec 8 '18 at 22:16
Garage SensorGarage Sensor
334
asked Dec 8 '18 at 22:16
Garage SensorGarage Sensor
334
334
add a comment |
add a comment |
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