Olympiad Corner: No. 373

[摘要] All natural numbers greater than 1 are coloured with blue or red sothat the sum of every two blue numbers (not necessarily distinct) is blue, and theproduct of every two red ones (not necessarily distinct) is red. It is known thatthe number 1024 is blue. What colour can the number 2017 be?OC432. Find the smallest natural number that is a multiple of 80 such thatyou can rearrange two of its distinct digits and the resulting number will also bea multiple of 80.

[学科分类] 数学（综合）