62nd Ukrainian National Mathematical Olympiad

Question

Find the integer that is closest to the value of the expression: ( (3 + 1)^2023 - ( 13 - 1 )^2023 ) ( (3 + 2)^2023 - ( 13 - 2 )^2023 ) ( (3 + 3)^2023 - ( 13 - 3 )^2023 ) ( (3 + 8)^2023 - ( 13 - 8 )^2023 ).

Accepted Answer

Let's consider the last factor: 13 - 8 = 3 + 89 - 8 = 3 + 8 (3 + 8)^2023 = (13 - 8)^2023, which means that the last factor equals 0, and therefore the whole product equals 0.