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In any set of 181 square integers, prove that one can always find a subset of 19 numbers, sum of whose elements is divisible by 19

In any set of 181 square integers, prove that one can always find a subset of 19 numbers, sum of whose elements is divisible by 19

Grade:Upto college level

1 Answers

manu saxena
46 Points
13 years ago

Hint: Note that there are just 10 quadratic residues in modulo 19; we can ?nd 19squares having the same remainder upon division by 19

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