Summing up the factors
Number Theory
Level
2
The number has exactly four prime factors. Find their sum.
The answer is 652.
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1 solution
note that
2 7 0 0 0 0 0 1 = 3 0 0 3 + 1 3 = ( 3 0 0 + 1 ) ( 3 0 0 2 − 3 0 0 + 1 )
= 3 0 1 ( ( 3 0 0 + 1 ) 2 − 3 ⋅ 3 0 0 ) = 3 0 1 ( 3 0 1 2 − 3 0 2 )
= 3 0 1 ( 3 0 1 − 3 0 ) ( 3 0 1 + 3 0 ) = 3 0 1 ( 2 7 1 ) ( 3 3 1 ) = 7 ∗ 4 3 ∗ 2 7 1 ∗ 3 3 1
so the answer is 7 + 4 3 + 2 7 1 + 3 3 1 = 6 5 2 .