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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>
-g(-2) is 10
<u>Step-by-step explanation:</u>
Step 1:
Given g(x) = 3x - 4. Find g(-2).
⇒ g(-2) = 3 × -2 - 4 = -6 - 4 = -10
Step 2:
Find -g(-2)
⇒ -g(-2) = -(-10) = 10
