Prove that among any 12 consecutive positive integers
there is at least one which is smaller than the sum of
its proper divisors. (The proper divisors of a positive
integer n are all positive integers other than 1 and n
which divide n. For example, the proper divisors of 14 are 2
and 7)
Answer
Hint: Among any $12$ consecutive positive integers, there is one that is a multiple of $12$.
Can you show that $12n$ is smaller than the sum of its divisors for any positive integer $n$?
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