22!+1=0 mod 23[as per Wilsons theorem prime (p-1)!+1=0 mod p]

=>22.21.20.19.18!+1=0 mod 23[in usual notation a=b mod n means a-b is divisible by n]

=>175560.18!+1=0 mod 23.............................1

 

175559=0 mod 23

=>18!.175559=0 mod 23

=>18!(175560-1)=0 mod 23

=>18!.175560-18!=0 mod 23..............................2

 

sutracting 2 from 1

175560.18!+1-(18!.175560-18!)=0 mod 23

18!+1=0 mod 23