Question 9: Sum of Factors and Difference of Squares
Number Theory
Level
2
Find the sum of all factors of 9991.
The answer is 10192.
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1 solution
9 9 9 1 = 1 0 0 0 0 − 9 = ( 1 0 0 + 3 ) ( 1 0 0 − 3 ) = 1 0 3 × 9 7 ,the factors are 1 , 9 7 , 1 0 3 , 9 9 9 1 ,sum: 1 + 9 7 + 1 0 3 + 9 9 9 1 = 1 0 1 9 2