Question 34722
LET THE 4 CONSECUTIVE INTEGERS BE N-1,N,N+1,N+2
THEIR PRODUCT = P =(N-1)N(N+1)(N+2)=(N^2-1)(N^2+2N)=N^4+2N^3-N^2-2N....IF THIS IS TO BE A PERFECT SQUARE THEN IT SHOULD BE IN THE FORM OF  
(N^2+AN)^2...SINCE THERE IS NO CONSTANT TERM IN P...EXPANDING
(N^2+AN)^2=N^4+2AN^3+A^2N^2..EQUATING WITH P WE SHOULD HAVE 
2A=1...OR...A=1/2
A^2=-1..AND -2N=0.....WHICH IS NOT POSSIBLE .....HENCE P CANNOT BE WRITTEN AS A PERFECT SQUARE.