If a is a factor of c and a + b = c, prove that a is a factor of b.

label Algebra
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May 8th, 2015

a is a factor of c , so c = ka for some integer k   (1)

a + b = c

So b = c -a

b = ka -a    Using  (1) and replacing c

b = (k-1) a Taking out a as common factor

Since k is an integer, k-1 is also an integer, call it m

b = ma  (where m = k-1)

b is a multiple of a , so a is a factor of b

May 8th, 2015

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May 8th, 2015
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