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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:12th Pass

1 Answers

sushant singh
66 Points
11 years ago

hey surendra i think this question is easy if you understand the fact of modulo

as  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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