I need to find the quotient and remainder when dividing 10^30 by 97.

When we divide 10^30 by 97, we need to find q and r such that:
10^30 = 97q + r, where 0 ≤ r < 97

To find the remainder, I'll use modular arithmetic to find 10^30 (mod 97).

First, I'll find a pattern in powers of 10 modulo 97:
- 10^1 ≡ 10 (mod 97)
- 10^2 ≡ 100 ≡ 3 (mod 97)
- 10^3 ≡ 30 (mod 97)
- 10^4 ≡ 300 ≡ 9 (mod 97)
- 10^5 ≡ 90 (mod 97)
- 10^6 ≡ 900 ≡ 27 (mod 97)

Let me find the order of 10 modulo 97 more systematically. I'll use the fact that 97 is prime, so by Fermat's Little Theorem, 10^96 ≡ 1 (mod 97).

Let me calculate 10^30 (mod 97) using repeated squaring:
- 10^1 ≡ 10 (mod 97)
- 10^2 ≡ 100 ≡ 3 (mod 97)
- 10^4 ≡ 9 (mod 97)
- 10^8 ≡ 81 (mod 97)
- 10^16 ≡ 81^2 = 6561 ≡ 67·97 + 62 ≡ 62 (mod 97)

Now I need 10^30 = 10^16 · 10^8 · 10^4 · 10^2:
- 10^16 ≡ 62 (mod 97)
- 10^8 ≡ 81 (mod 97)
- 10^4 ≡ 9 (mod 97)
- 10^2 ≡ 3 (mod 97)

So 10^30 ≡ 62 · 81 · 9 · 3 (mod 97)

Let me calculate step by step:
- 62 · 81 = 5022 = 51·97 + 75 ≡ 75 (mod 97)
- 75 · 9 = 675 = 6·97 + 93 ≡ 93 (mod 97)
- 93 · 3 = 279 = 2·97 + 85 ≡ 85 (mod 97)

Therefore, the remainder is 85.

To find the quotient, I use:
q = (10^30 - r)/97 = (10^30 - 85)/97

The quotient is:
q = (10^30 - 85)/97 = (1000000000000000000000000000000 - 85)/97

Calculating this:
q = 999999999999999999999999999915/97
q = 10309278350515463917525773093

Therefore:
- Quotient: 10309278350515463917525773093
- Remainder: 85
