Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Sum of squares of two numbers.
Which of the following numbers can be expressed as the sum of squares of two integers
Pythagorus Theorem
Integers
Algebra
Answer: none of these
B.Stat Objective Question 77
Challenges and Thrills of Pre-College Mathematics by University Press
1995 not perfect square cannot be expressed as sum of perfect squares by pythagoras theorem
1999 not perfect square cannot be expressed as sum of perfect squares by pythagoras theorem
2003 not perfect square cannot be expressed as sum of perfect squares by pythagoras theorem then none of these integers.
I.S.I. & C.M.I. Entrance Program
Taught by students and alumni of I.S.I. & C.M.I.
Example For 5 is not Perfect Square ,yet is SUM Of Two Perfect Squares;
5=1^2+2^2;
So Reasoning Given Above For 1995;1999&2003 :NOT perfect square cannot be expressed as sum of perfect squares by pythagoras theorem then none of these integers.SEEMS TO BE CORRECT;
1995-1^2=1994; 1995-2^2=1991; 1995-3^2=1986; 1995-4^2=1979; 1995-5^2=1970;....
1995-k^2=Not Perfect Squares
Reasoning Given Above By Cheenta Does Not Seem To Be Correct!