Prove using what you know about modular arithmetic that the

Prove using what you know about modular arithmetic that the product of any 4 consecutive integers is always divisible by 6.

let any 4 consecutive integers be in form

n,n+1,n+2 , n+3

their product would be in form = n*(n+1)*(n+2)*(n+3)

In every consecutive 4 no\'s there will be , there will be two no.\'s which will be divided by 2 and atleast one no. divisible by 3.

If we put any odd no. as n in above equation , there will be one or more no. divisble by 3 and and two no. divisible by 2

In case we put even no. as n , there will be exactly one no. divisble by three and two no\'s divisible by 2.

If the no. is both divisible by 2 and 3 , it will be divisible by 6

so ,product of every 4 consecutive integer will divisible by 6