AMCAMC 122020 AMC 12A2020 AMCAMC 12 Arelatively primenumber theory
Problem Statement
The number a=qp, where p and q are relatively prime positive integers, has the property that the sum of all real numbers x satisfying ⌊x⌋⋅{x}=a⋅x2 is 420, where ⌊x⌋ denotes the greatest integer less than or equal to x and {x}=x−⌊x⌋ denotes the fractional part of x. What is p+q?<spanclass=′latex−bold′>(A)</span>245<spanclass=′latex−bold′>(B)</span>593<spanclass=′latex−bold′>(C)</span>929<spanclass=′latex−bold′>(D)</span>1331<spanclass=′latex−bold′>(E)</span>1332