Assume a is not divisible by 10. (otherwise the problem is trivial).
<span>Define R(m) to be the remainder of a^m when divided by 10. </span>
<span>R can take on one of 9 possible values, namely, 1,2,...,9. </span>
<span>Now, consider R(1),R(2),......R(10). At least 2 of them must have the sames value (by the Pigeonhole Principle), say R(i) = R(j) ( j>i ) </span>
<span>Then, a^j - a^i is divisible by 10.</span>
The answer is the second option, or Ray BE is a bisector of angle ABE.
Answer:
One solution
Step-by-step explanation:
Answer:
The Bill of Rights was added to the Constitution in the form of amendments. The chief purpose of the amendments was to protect the rights of individuals from the government's interference. They guarantee rights such as religious freedom, freedom of the press, and trial by jury to all American citizens.
Step-by-step explanation:
Answer:
Dalton didn't ride any kilometer farther since he keeps threading in the same path as that of his father.
Step-by-step explanation:
If Dalton's dad rode 1 kilometer north, 2 kilometers west 1 kilometer south and 2 kilometers east, then he has been moving in a rectangular path.
If Dalton rode in the same path 5times, then Dalton's has not move farther than his dad since he is still moving in the same rectangular path. He is only expending more energy.
Their final destination will still be the same for both of them no matter how many times Dalton keeps threading in the same path.
