3. Suppose that a positive integer is written in decimal notation as n = akak-1… a2a1a0 where 0 ai 9. Prove that n is divisible
by 9 if and only if the sum of its digits ak + ak–1 + … + a1 + a0 is divisible by 9.
1 answer:
Answer:
Therefore n is divisible by 9 if and only if is also divisible by 9.
Step-by-step explanation:
Given number is
This means
Here we need to prove
is divisible by 9.
We know that
10 ≡ 1 mod 9
It means if 10 divides by 9 the remainder = 1.
mod 9
mod 9
Therefore n is divisible by 9 if is also divisible by 9.
And conversely is also true.
Therefore n is divisible by 9 if and only if is also divisible by 9.
You might be interested in
Answer: Prime
Step-by-step explanation:
its only factors are 1 and 7
Answer:
8) 125
9) 16 1/2
Step-by-step explanation:
8) Image below
9) 2.75 x 3 x 2 = 16.5
x adds 1 and y subtracts by 6
Answer:
0.005
this is because 5 has to be pushed back 3 times
Depends on how many bottles we collected each day