# Positive integer proof

Problem: Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive?

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Proof: (This is a constructive proof)

Suppose there exists such a positive integer n, such that it is the sum of the positive integers not exceeding it.

I need to make clear of the term "not exceeding".

By my understanding, it means "not bigger than" or "less than or equal to".

Now by this understanding, the integer n ...

#### Solution Summary

This provides an example of a positive integer proof.

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Proof of Infinite Positive Integers

Prove: There are infinitely many prime numbers p of the form 4n+3. In other words, show that there exist infinitely many positive integers, n, such that the number 4n+1 is prime.

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