Let-P-x-be-polynomial-in-x-with-integral-coefficients-If-n-is-a-solution-of-P-x-0-mod-n-and-a-b-mod-n-prove-that-b-is-also-a-solution-

Question Number 76229 by arkanmath7@gmail.com last updated on 25/Dec/19

L e t P (x) b e p o l y n o m i a l i n x w i t h i n t e g r a l

c o e f f i c i e n t s . I f n i s a s o l u t i o n o f

P (x) \equiv 0 (m o d n), a n d a \equiv b (m o d n),

p r o v e t h a t b i s a l s o a s o l u t i o n .

Answered by Rio Michael last updated on 25/Dec/19

g e n e r a l l y i f a \equiv b (m o d n) t h e n n ∣ (a - b)

i f n ∣ (a - b) a n d n ∣ p (x) f r o m p (x) \equiv 0 (m o d n)

t h e n (a - b) i s a l s o a s o l u t i o n

n o w i f a \equiv b (m o d n) t h e n b \equiv a (m o d n)

w h i c h m e a n s a \equiv b (m o d n) h e n c e a a n d b

a r e s o l u t i o n s t o p (x) \equiv 0 (m o d n)

h e n c e b i s a s o l u t i o n .

Commented by arkanmath7@gmail.com last updated on 25/Dec/19

t h n x s i r