1. **Problem Statement:** Determine the day of the week for March 14, 1988, given that March 14, 2021 was a Sunday. 2. **Formula and Explanation:** We use modular arithmetic to find the day difference modulo 7 because there are 7 days in a week. The formula is: $$\text{Day}_{1988} \equiv \text{Day}_{2021} - 365 \times (2021 - 1988) - \text{leap years} \pmod{7}$$ where each year contributes 365 days and each leap year adds an extra day. 3. **Calculate total years and leap years:** - Total years between 1988 and 2021: $2021 - 1988 = 33$ - Number of leap years in this span: 8 4. **Substitute values:** $$\text{Day}_{1988} \equiv 0 - 365 \times 33 - 8 \pmod{7}$$ Since March 14, 2021 is Sunday, we represent it as 0 mod 7. 5. **Simplify the expression:** Calculate $365 \times 33 = 12045$ So, $$\text{Day}_{1988} \equiv -12045 - 8 = -12053 \pmod{7}$$ 6. **Reduce modulo 7:** Find $-12053 \bmod 7$ Since $12053 \div 7 = 1721$ remainder $6$, then $$-12053 \equiv -6 \equiv 1 \pmod{7}$$ 7. **Interpret result:** $1 \pmod{7}$ corresponds to Monday (since 0 is Sunday). **Final answer:** March 14, 1988 was a Monday.