Answer is (A) 2k/n
n = 10k + r, k, r ∈ N, 0 ≤ r ≤ 9
Unit place of a2 will contain 0, 1, 4, 5, 6, 9 only.
Hence, a2 – 1 is divisible by 10 only if unit place of a2 contain 1.
If unit place of a2 is 1, then unit place of a will be 1 or 9.
n = 10k + r
r = 0
n = 10k, no. of a whose unit place is 1 or 9
⇒ k = 1, n = 10, no. of a whose unit place is 2
⇒ k = 2, n = 20, no. of a whose unit place is 4
⇒ k = k, n = 10k, no. of a whose unit place is 2k
Therefore
pn = 2k/n