How a^3 - a is divisible by 6 ?

Proof | a^3 - a is divisible by 6 | a - Positive Integer

This is an important identity which one should be aware of because it can come in handy anytime , thus we in this video we will proof that how a^3 - a is divisible by 6, where a is a positive integer.

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The problem discussed in the video :

Proof | a^3 - a is divisible by 6 | a - Positive Integer

The solution to the problem: Follow the following steps,

1. a^3 - a can be written as a ( a -1 ) ( a + 1 )
2. This can be written as three consecutive integers ( a - 1) a (a + 1 )
3. We know that the product of three consecutive integers is always of the form 6k , so we can say that a^3 - a is divisible by 6 .

Practice Question at the end :

Prove that p^2 -1 is divisible by 24 if p is a prime number greater than 3.

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