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>
Answer:
the diameter is: 14
the circumference is: C≈43.98
the area is: A≈153.94
Step-by-step explanation:
1 cm = 20 km
so 3.5 cm would equal : 3.5 * 20 = 70 km <==
The answer is D. the amount of fabric needed for each pair of shorts.
Answer:
Step-by-step explanation:
need to multiply outsides into the parenthesis
and then combine like terms and you get
-34x+71
