prove-that-if-a-and-c-are-odd-integers-then-ab-bc-is-even-for-every-integer-b-

Question Number 143630 by Eric002 last updated on 16/Jun/21

p r o v e t h a t i f a a n d c a r e o d d i n t e g e r s

t h e n a b + b c i s e v e n f o r e v e r y i n t e g e r b ?

Commented by mr W last updated on 16/Jun/21

y e s .

a, c = a d d

\Rightarrow a + c = e v e n

e v e n \times a n y i n t e g e r = e v e n

\Rightarrow (a + c) b = e v e n

Answered by Rasheed.Sindhi last updated on 16/Jun/21

L e t a = 2 m + 1 & c = 2 n + 1

a b + b c = b (a + c) = b (2 m + 1 + 2 n + 1)

= b (2 m + 2 n + 2)

= 2 b (m + n + 1) (E v e n)