How to prove n-degree unary equation by algebraic method

Let me give you a few examples first.

When a = 1, b = 2 and n = 2, a n+b n = 1 2+2 2 = 5, a 2-b 2 = 1 2-2 2 =-3,

When a = 2, b = 3 and n = 3, an+b n = 2 3+3 3 = 35, an-b n = 2 3-3 3 =-19,

When a = 4, b = 3 and n = 5, a n+b n = 4 5+3 5 = 1267, a n+b n = 4 5-3 5 = 78 1.

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By analogy, we can draw such a conclusion.

That is, when n is odd, a n+b n = (a+b) [(a (n-1)-a (n-2) b+a (n-3) b 2-+(-b) (n-).

When n is an even number, generally speaking, a n+b n cannot be further deformed. For example, A 2+B 2, A 4+B 4, a6+B6 =(a2+B2)[a4-(AB)2+B4]. ......

hope this helps

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