MathDB

2015 Algebra #2: Partial Fraction Decomposition

Source:

March 28, 2015

algebrapartial fractions

Problem Statement

The fraction

\tfrac1{2015}

has a unique "(restricted) partial fraction decomposition'' of the form

\dfrac1{2015}=\dfrac a5+\dfrac b{13}+\dfrac c{31},

where

a

b

, and

c

are integers with

0\leq a<5

and

0\leq b<13

. Find

a+b