Rowan Huynh
2022-04-30
Answered

Proving the generator of

$A=\{154a+210b:a,b\in \mathbb{Z}\}$ is $(154,\text{}210)$

You can still ask an expert for help

August Moore

Answered 2022-05-01
Author has **17** answers

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

$a,\text{}b\in \mathbb{Z}$

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.

For the further proof , you just need to show that

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

for a particular choice of a and b . And HCF obviously generate all the common multiples then.

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