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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

- 1995
- none of these
- 1999
- 2003

Pythagorus Theorem

Integers

Algebra

But try the problem first...

Answer: none of these

Source

Suggested Reading

B.Stat Objective Question 77

Challenges and Thrills of Pre-College Mathematics by University Press

First hint

1995 not perfect square cannot be expressed as sum of perfect squares by pythagoras theorem

Second Hint

1999 not perfect square cannot be expressed as sum of perfect squares by pythagoras theorem

Final Step

2003 not perfect square cannot be expressed as sum of perfect squares by pythagoras theorem then none of these integers.

- https://www.cheenta.com/rational-number-and-integer-prmo-2019-question-9/
- https://www.youtube.com/watch?v=lBPFR9xequA

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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!