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


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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

	$L e t a = 2 m + 1 & c = 2 n + 1$ $a b + b c = b (a + c) = b (2 m + 1 + 2 n + 1)$ $= b (2 m + 2 n + 2)$ $= 2 b (m + n + 1) (E v e n)$
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