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Four factors (Posted on 2015-11-06) Difficulty: 2 of 5
Let N = 111 ... 1222 ... 2, i.e. 1999 digits of digit 1 followed by 1999 digits of 2.

Express N as a product of four integers, none of them equal to 1.

No Solution Yet Submitted by Ady TZIDON    
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Solution by induction, not rigorous Comment 2 of 2 |
111222 = 2*3*167*111
11112222 = 2*3*1667*1111
1111122222 = 2*3*16667*11111

If there are 1999 1's and 1999 2's, then four numbers which multiply to this are:

2
3
1...1997 6's...7
1999 1's

Only the 2 and the 3 are guaranteed to be prime.

  Posted by Charlie on 2015-11-06 09:56:37
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