- #1
The Subject
- 32
- 0
Member warned that the homework template is not optional
Hi I'm reading a text about modular arithmetic,
Prove that 16^43 - 10^26 actually is divisible by 21.
They separate it by showing it is divisible by 7 and 3
they showed [tex] 16 \equiv 2 \textrm{ mod 7} \\
16^2 \equiv 2^2 \equiv 4 \textrm{ mod 7} \\
16 \equiv 2^3 \equiv 1 \textrm{ mod 7} \\ [/tex]
So there is a pattern of length 3.
They later made 43 = 3 * 14 +1 . so,
[tex]
16^{43} \equiv 16^1 \equiv 2 \textrm{ mod 7} \\ [/tex]
whats the reasoning with 43 = 3 * 14 + 1 ?
Prove that 16^43 - 10^26 actually is divisible by 21.
They separate it by showing it is divisible by 7 and 3
they showed [tex] 16 \equiv 2 \textrm{ mod 7} \\
16^2 \equiv 2^2 \equiv 4 \textrm{ mod 7} \\
16 \equiv 2^3 \equiv 1 \textrm{ mod 7} \\ [/tex]
So there is a pattern of length 3.
They later made 43 = 3 * 14 +1 . so,
[tex]
16^{43} \equiv 16^1 \equiv 2 \textrm{ mod 7} \\ [/tex]
whats the reasoning with 43 = 3 * 14 + 1 ?