# Solve the following equation in natural numbers : #x²+y²=1997(x-y) #?

The following proof is based on that in the book "An Introduction to Diophantine Equations: A Problem-Based Approach" by Titu Andreescu, Dorin Andrica, Ion Cucurezeanu.

Given:

Then:

Hence we find:

In addition note that:

Hence:

We find:

So:

or

and hence:

and hence:

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The solutions for the equation (x^2 + y^2 = 1997(x - y)) in natural numbers are (x = 49) and (y = 5).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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