When you ran out of ideas.

Algebra Level 4

Positive integers m m and n n satisfy:

1 = a 1 m ( a 1 − a 2 ) ( a 1 − a 3 ) ⋯ ( a 1 − a n ) + a 2 m ( a 2 − a 3 ) ( a 2 − a 4 ) ⋯ ( a 2 − a 1 ) + ⋯ + a n m ( a n − a 1 ) ( a n − a 2 ) ⋯ ( a n − a n − 1 ) 1 = \frac{a_1^m}{(a_1 - a_2)(a_1 - a_3) \cdots (a_1 - a_n)} + \frac{a_2^m}{(a_2 - a_3)(a_2 - a_4) \cdots (a_2 - a_1)} + \cdots + \frac{a_n^m}{(a_n - a_1)(a_n - a_2) \cdots (a_n - a_{n - 1})}

What is m m ?

None of the others. n + 1 n + 1 n − 1 n - 1 m ∈ ∅ m \in \varnothing Cannot be determined. n n

Thành Đạt Lê by Thành Đạt Lê , 17, Singapore

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