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>
Hello I hope this helps. I'm pretty sure this is the answer.
Part A: C
Part B: A
Answer:
67
Step-by-step explanation:
100 - 33 = 67
The difference between 100 and 33 is 67.
Answer:
15 thirds divided by 3 = 1.66666667
Step-by-step explanation:
