don steward
mathematics teaching 10 ~ 16

Monday, 10 January 2011

Craig's conjecture

Craig, a capable 13 year old, was exploring how many factors numbers of the form
(p^n) x (q^m) have, where p and q are both prime:

400 has 15 factors (1,2,4,5,8,10,16,20,25,40,50,80,100,200,400)

100 has 9 factors

72 has 12 factors

20 has 6 factors

with several  more examples he came up with the general rule:
add the powers (of the two primes), multiply by 3 then - 3

his rule works quite often
for certain special cases all the time
but what is the limitation for his conjecture?

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