Divisibility problem

[steep oracle]

I had an idea to use pigeonhole principle so that if there is some number = 0(mod2024) we're done so let's assume there isn't so we know there are two numbers which remainders are the same but it doesn't give a sol.

Another idea was to go further and assume that if there are not 2 numbers such that their sum is 0 (mod2024) then we know that at least 1012 remainders are not in our set (and 0 is neither), so from pigeonhole we know there are 3 numbers which remainders are the same but it seams like a dead end

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[obtuse narwhal]

write the numbers as a_1, …, a_2024

now think about the partial sums
a_1
a_1 + a_2
….
a_1 + … + a_2024

now apply your first idea to this collection instead and you’re close to done

[regal cobalt]

@steep oracle

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