Difference between revisions of "2018 USAJMO Problems/Problem 5"
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| − | + | ==Problem 5== | |
| + | Let <math>p</math> be a prime, and let <math>a_1, \dots, a_p</math> be integers. Show that there exists an integer <math>k</math> such that the numbers <cmath>a_1 + k, a_2 + 2k, \dots, a_p + pk</cmath>produce at least <math>\tfrac{1}{2} p</math> distinct remainders upon division by <math>p</math>. | ||
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| + | ==Solution== | ||
Revision as of 02:03, 21 April 2018
Problem 5
Let 
be a prime, and let 
be integers. Show that there exists an integer 
such that the numbers ![\[a_1 + k, a_2 + 2k, \dots, a_p + pk\]](http://latex.artofproblemsolving.com/7/6/2/7624ce20fc9bfb798126ffacdb34110159ef0094.png)
produce at least 
distinct remainders upon division by .
