13. (12 points) A page from the middle of a book has been torn out, and the sum of the remaining page numbers is 1133. What are the two page numbers on the torn-out page?



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【Solution】Solution: First estimate between 40 - 50
The sum of numbers from 1 to 40 is $40(1+40) \div 2=820$, and the sum of numbers from 1 to 50 is $50(1+50) \div 2=1275$
Since $820<1133,1133<1275<1133+49+50$
Then estimate between 47 - 51
The sum of numbers from 1 to 47 is $47(47+1) \div 2=1128<1133$ (discard)
(1) The sum of numbers from 1 to 48 is $1128+48=1176$
$$
1176-1133=43
$$
43 is the sum of two consecutive integers 21, 22
Therefore, there are 48 pages in total, and the pages torn out are 21, 22
(2) The sum of numbers from 1 to 49 is $1176+49=1225$
$$
1225-1133=92
$$

Not the sum of two consecutive integers (discard)
In summary, there are only 48 pages, and the pages torn out are 21, 22