Arun
Last Activity: 6 Years ago
a) is wrong
Consider k = 3.
10^(k+1) + 1 = 10^4 + 1 = 10001
Clearly, 11 does NOT divide 10001 since 10001/11 = 909.18
But, a3 = 1010101 is composite since it is divisible by 101.
(b) is wrong
Consider k = 2.
10^(k+1) - 1 = 10^3 - 1 = 999
Clearly, 11 does NOT divide 999 since 999/11 = 90.82
But, a2 = 10101 is composite since it is divisible by 3.
(c) is wrong
Consider k = 4.
k - 2 = 4 - 2 = 2, which is NOT divisible by 3.
But, a4 = 101010101 is composite since it is divisible by 41.
So, (d) is your only choice left, even though it might be a bit hard to prove.
