Olympiad Maths Prep

Track / Stage 4 / 43 of 340 #303 of 2000

Problem 303

AMC 12 late, AIME early
Number theory Difficulty 4.6 Find the answer

[ Divisibility rules (etc.).]

Come up with divisibility rules for natural numbers by a) 2; b) 5; c) 3; d) 4; e) 25.

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

See tasks 30610,30612,3061730610, \underline{30612,} 30617.

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