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Part of 2013 Bundeswettbewerb Mathematik

Problems(2)

BWM 2013 P1: Basic combinatorics

Source:

Is it possible to partition the set

S=\{1,2,\ldots,21\}

into subsets that in each of these subsets the largest number is equal to the sum of the other numbers?

BWM 2013 P5: mn|(m^2+n^2+m)

Source:

m

n

are positive integers such that

m^2+n^2+m

is divisible by

mn

m

is a square number.