The statement about a positive integer being expressed as the sum of the squares of 2 positive integers has been proved below.
- Positive integers are simply positive whole numbers. They don't include fractions or decimals. Examples of positive integers are; 1, 2, 3, 4, 5.....e.t.c.
- Now, we want to prove that there is a positive integer that can be expressed as the sum of squares of positive integers.
For example;
a² + b² = c
where a, b and c are positive integers
If we use a = 2 and b = 4, we will have;
2² + 5² = c
c = 4 + 25
c = 29
- Now, we can see that the sum of the squares of the positive integers 2 and 5 also yielded a positive integer 29.
- Also, we see the facts that, the square of the positive integer 2 gave us a positive integer 4.
- Also, the square of the positive integer 5, gave us a positive integer 25.
- Thus, the sum of both positive integers gave us a positive integer 29 and the statement in the question is proved.
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