Do you think an increase in both debtors and creditors' payment period could result in an increase in working capital? Why ?

If both debtors and creditor increase with the same amount then net change in working capital is zero. So working capital does not change if both increase with the same amount.

no 

working capital = current assets - current liabilities

Increase in debtors would effect the increase in current assets this would effect increase in the working capital needs  and increase in creditors payment period would increase the current liabilities of the company and this would effect decrease in working capital needs.

Hence the statement is partially correct the extent increase in debtors would result in increase in working capital however an increase in  creditors payment period would effect reduction in working capital.