Maths Olympiad Prep

Track / Stage 4 / 151 of 340 #411 of 1964

Problem 411

AMC 12 late, AIME early
Number theory Difficulty 4.8 Find the answer

47. The greatest common divisor of four numbers has been found; how can we quickly select three more numbers so that the found greatest common divisor remains the greatest common divisor of all seven numbers?

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Official solution

47. It is enough to multiply the greatest common divisor of the given numbers by any three numbers and add the resulting products to the given numbers.

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