# Proving the generator of A = \{154a + 210b : a,b

Proving the generator of
$A=\left\{154a+210b:a,b\in \mathbb{Z}\right\}$ is
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August Moore
Step 1
For the further proof , you just need to show that
$154a+210b$
just generates all the common multiples of 154 and 210 for different values of a and b where

and even HCF can also be written in in the form
$154a+210b$
for a particular choice of a and b . And HCF obviously generate all the common multiples then.