Problem:
The expression 20202021−20212020 is equal to the fraction qp, where p and q are positive integers whose greatest common divisor is 1. What is p?
Answer Choices:
A. 1
B. 9
C. 2020
D. 2021
E. 4041
Solution:
We write the given expression as a single fraction:
20202021−20212020=2020⋅20212021⋅2021−2020⋅2020
by cross multiplication. Then by factoring the numerator, we get
2020⋅20212021⋅2021−2020⋅2020=2020⋅2021(2021−2020)(2021+2020)
The question is asking for the numerator, so our answer is 2021+2020=4041, giving (E)4041
The problems on this page are the property of the MAA's American Mathematics Competitions