i got a question from a class teacher,nobody in the class or in the higher class can do it,because,number system is not in our syllabus.but i wanna know,let a=<3^n+2n+1>,where n can be any of positive numbers.the question is for which values of n;a can be a perfect square?oh,can anyone tell me about a book of number system where i can learn by ownself?

You could experimentally see if you can find some solutions using a computer. Have you found any solutions?

If you have access to excel or openoffice/calc you can easily set up a test for a from 1 to 25 before the numbers get so big that excel might start approximating in display and might confuse you. Set up column A as a from 1 to 20, B1 as =3^A1 etc, C1 as =2*A1, D1 as =1, E1 = +B1+C1+D1, F1 as =Sqrt(E1). Copy down 24 rows and you have an idea.