Competition problem — Number theory

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Number theory Difficulty 6.1 National olympiad Prove it

21. a) Show that if $a$ and $b$ are positive integers then $(a, b)=(a+b,[a, b])$ .
b) Find the two positive integers with sum 798 and least common multiple 10780.

Solution

21. 308,490

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