15. March 19, 2017 was a Sunday, based on this, calculate what day of the week September 1, 2017 was.

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【Analysis】First, calculate the number of days from March 19 to September 1, then determine how many weeks and extra days are in this period, and finally judge based on the remainder.

【Solution】Solution: From March 19 to March 31, there are:
$$
31-19=12 \text { (days) }
$$
April and June have 30 days, May, July, and August have 31 days, in total:
$$
\begin{array}{l}
30 \times 2+31 \times 3+12+1 \\
=60+93+13 \\
=166 \text { (days) }
\end{array}
$$
$$
166 \div 7=23 \text { (weeks) } \cdots 5 \text { (days) }
$$

Therefore, if March 19 is a Sunday, September 1 is a Friday.
Answer: September 1, 2017 is a Friday.
So the answer is: Friday.
【Comment】To solve this type of problem, first calculate the number of days passed, then determine how many weeks and extra days are in this period, and finally deduce based on the remainder.