Catalan med-hard
a and b are natural numbers such that
b a = 1 − 2 1 + 3 1 − 4 1 + . . . − 2 0 1 4 1 + 2 0 1 5 1
Is it true that a is divisible by 3023?
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1 solution
You have to mention in your posted problem that a and b are positive coprime integers. Because b a = 3 0 2 3 b 3 0 2 3 a and 3 0 2 3 a is also an integer and is divisible by 3023 even though a is not divisible by 3023.
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This only becomes a problem if the answer were "No". He should restrict them to being coprime (so that one cannot find the answer in the meta), but the answer is the same whether we assume they're coprime or not.