I have the following task:
Prove, that four different square numbers can't create an arithmetic sequence(obviously, the $0,0,0,0$ case is forbidden).
How can I prove this statement? I tried to write down the numbers in their form: $a<b<c<d \rightarrow a^2 , b^2, c^2, d^2$ is my sequence, and this can't occur:
$b^2-a^2=D, c^2-b^2=D, d^2-c^2= D, D \in \mathbb{N^+}$ is a fixed number. What should I do after this? Summing the equations didn't really help me to go further.
Thanks in advance for the help.
