Stirling approximation here.

Algebra Level 4

The 2018 2018 positive numbers a 1 , a 2 , . . . , a 2018 a_1, a_2, ..., a_{2018} satisfy the inequality a i a j ≤ i + j a_i a_j \le i + j for all distinct indices i , j i, j . Determine the largest possible value of the product a 1 a 2 . . . a 2018 a_1 a_2 ... a_{2018} .

2 × 12 × . . . × 4040 2\times 12\times ...\times 4040 3 × 7 × . . . × 4035 3\times 7\times ...\times 4035 Can't be evaluated . Question incomplete 5 × 11 × . . . × 4030 5\times 11\times ...\times 4030 4 × 8 × . . . × 4036 4\times 8\times ...\times 4036

Priyanshu Mishra by Priyanshu Mishra , 20, India

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