+23 Find the largest prime factor of 1,005,010,010,005,001.
Can someone do this with algebra?
+1786 We have to make a really important observation to solve this problem. Note that
\(1,005,010,010,005,001 = \\ 1\times 10^{15} + 5 \times 10^{12} + 10\times 10^9 + 10\times 10^6 + 5 \times 10^3 + 1\times 10^0\\ \)
This value is equal to
\((10^3+1)^5\), which is equal to \(1001^5\)
Now, we have to find the largest prime factor of 1001.
We know that \(1001=13*11*7\)
This means the largest prime factor is 13.
Thanks! :)
