Prove that number is square of natural We have number $a=246810...98100 $. Number $a$ consists of the following even numbers from $2 -100$ . Decide whether number is a square. 
I was given a hint to this task to sum all digits. 
Also I would be grateful if someone could explain whether this rule is true: If the sum of digits is divided by $k^2$ then this number is square of natural

Add up all the digits in your number. What do you get? Is the total divisible by three? Is it divisible by nine? The answers to these two questions will tell you what you want to know. (This is not a general method, but it works in this particular case.)
And no, your last sentence is certainly not true. Take 13, for instance.
