A cool discovery

Our young friend, all of 6 years old now, made a cool conjecture: for all k, for all n >= k, the last k digits of 2^n are the same as those of 2^(n + 4 * 5^(k-1)), and that this is not the case for any power of 2 between these two. He verified this for k = 1 and 2, and then guessed and verified it for k=3, which is truly amazing, as his conjecture would then be that the last three digits of 2^103 are 008. This is not particularly easy to verify! (Note that he does not know enough algebraic notation to write it out this way, but he came up with the expression all by himself.)

The conjecture can be proved using some simple number theory, but for a 6 year old to discover this ...

Other interesting problems he solved before: Find the number of integers between 0 and 1000 that can be written as the difference of two squares? Ans: 751.
What numbers with all digits repeated are primes? He figured out that the only non-trivial such primes must have the digit 1 repeated a prime number of times.
Of course these problems seem trivial in the light of the above conjecture, but I was very impressed at the time. He has also started reading Recreations in the Theory of Numbers by Albert Beiler, and likes Raymond Smullyan's logic puzzle books.