Answer:
shown below
Step-by-step explanation:
18) 4 x 1 = 4, 7 x 2 = 14, 4/14
19) 15 x 2 = 30, 2 x 20 = 40, 30/40
20) 3 x 7 = 21, 6 x 8 = 48, 21/48
21) 9 x 1 = 9, 10 x 2 = 20, 9/20
22) 3 x 2 = 6, 6 x 4 = 24, 6/24
Answer: need the options you choos frome
Step-by-step explanation:
Hizo contribuciones sustanciales a la teoría analítica de los números y trabajó en funciones elípticas, fracciones continuas y series infinitas.
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>