2024 AMC 10B Problems/Problem 7

Problem

What is the remainder when $7^{2024}+7^{2025}+7^{2026}$ is divided by $19$ ?

$\textbf{(A) } 0 \qquad\textbf{(B) } 1 \qquad\textbf{(C) } 7 \qquad\textbf{(D) } 11 \qquad\textbf{(E) } 18$

We can factor the expression as

$7^{2024} (1 + 7 + 7^2) = 7^{2024} (57).$

Note that $57$ is divisible by $19$ , this expression is actually divisible by 19. The answer is $\textbf{(A) } 0$ .

2024 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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