Difference between revisions of "2018 USAJMO Problems/Problem 5"
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+ | Notice that, if <math>a_i + ik\equiv a_j + jk\text{ (mod } p\text{)}</math> for some <math>k\in {1, 2, ..., p},</math> then <math>a_i + ik\equiv a_j + jk\text{ (mod } p\text{)}</math> is false for all other <math>k'\in {1, 2, ..., p}.</math> |
Revision as of 02:35, 21 April 2018
Problem 5
Let be a prime, and let
be integers. Show that there exists an integer
such that the numbers
produce at least
distinct remainders upon division by
.
Solution
Notice that, if for some
then
is false for all other