Question
Mathematics Question on types of differential equations
The remainder when (2021)2022 + (2022)2021 is divided by 7 is
A
0
B
1
C
2
D
6
Answer
0
Explanation
Solution
The correct answer is (A):
(2021)2022+(2022)2021
= (7k-2)2022+(7k-1)2021
= [(7k-2)3]674+(7k1)2021-2021(7k1)2020+...-1
= (7k2-1)674 + (7m-1)
= (7n+1)+(7m-1)
= 7(m+n)(multiple of 7)
∴ Reminder = 0