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think of it as a thousand piece puzzle bro. Obviously it has no practical value but it’s just a puzzle to solve. That’s what the math Olympiad is all about
This problem is instructive. As shown, n^4 + 4 factors using a form of the Sophie Germain identity, something that shows up in math competitions. It is proved by completing the square then taking the difference of two squares to produce two factors for each expression. Following this, you have a product that telescopes. Again a technique you will see again. (consider the simplification of binomial coefficients). In more advanced math you *will* see completing the square, difference of squares and telescoping products (and sums) again. Now you have more tools in your toolbox!
