could somebody please help these maths problems:

Reduce the following fraction to its simplest form 1319977/1884823

and

Find all the pairs of integersmandnsuch that 89m+ 53n= 1

Thanks

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- Sep 20th 2008, 03:01 AMmaths777reduce fraction
could somebody please help these maths problems:

Reduce the following fraction to its simplest form 1319977/1884823

and

Find all the pairs of integers*m*and*n*such that 89*m*+ 53*n*= 1

Thanks - Sep 20th 2008, 03:10 AMMatt Westwood
"reducing a fraction to its simplest form" means "cancel out any common factors of the numbers on the top and the bottom".

For example, $\displaystyle \frac 4 6$ has a common factor of $\displaystyle 2$ as $\displaystyle \frac 4 6 = \frac {2 \times 2} {2 \times 3} = \frac 2 3$.

In the example given, I presume you're supposed to use the Eclidean algorithm to get the highest common factor of the two numbers given. You can then cancel out (i.e. divide both top and bottom) by that factor.

From the form of the second part of the question, I assume you're studying basic number theory, in which case you ought to have covered these aspects in your course work.