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Problem 403

AMC 12 late, AIME early

Number theory Difficulty 4.8 Find the answer

17. $a, b, c$ are three prime numbers greater than 3, then among the following judgments, the one that is definitely correct is ( ).
A. $a+b+c$ is an even number
B. $a^{2}+b^{2}+c^{2}$ is an even number
C. $a+b+c$ is a multiple of 3
D. $a^{2}+b^{2}+c^{2}$ is a multiple of 3

Your answer

Official solution

Reference answer: D

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.