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Difference of fractions and squares

Source: 2021 Fall AMC10B P3

November 17, 2021
AMCAMC 10AMC 10 B

Problem Statement

The expression 20212020−20202021\frac{2021}{2020} - \frac{2020}{2021} is equal to the fraction pq\frac{p}{q}, where pp and qq are positive integers whose greatest common divisor is 11. What is pp?
<spanclass=′latex−bold′>(A)</span>1<spanclass=′latex−bold′>(B)</span>9<spanclass=′latex−bold′>(C)</span>2020<spanclass=′latex−bold′>(D)</span>2021<spanclass=′latex−bold′>(E)</span>4041<span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span>9\qquad<span class='latex-bold'>(C) </span>2020\qquad<span class='latex-bold'>(D) </span>2021\qquad<span class='latex-bold'>(E) </span>4041
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