1*2*3*4 +1^4= 25=5^2
3*5*7*9 +2^4=961=31^2
10*15*20*25+5^4=75,625=275^2

Now prove:

The product of four consecutive terms of an arithmetic progression of integers* added to the fourth power of the common difference is always a perfect square.

*Applies to rational numbers in general.