This Olympiad questions states:
[Show that every term of the sequence 10001, 100010001, 1000100010001, ... is composite.]
Well, I figured out this sequence is generalised as an = 10001n for all n 1.
After actually doing this division in Excel(I know... I cheated), I found out the prime factorisation of 10001 = 73*137, hence proving the claim.
If I had no access to Excel, how would you have come up with this factorisation. Any results we can make use of to get the prime factorisation?