Let P(X,A) be the number of positive divisors of A not greater than X; for example, P(1,12)=1, P(2,12)=2, and P(12,12)=6.

1)If P(12,A)=7 and P(A,A)=10, what's A?

2)If x*y is a divisor of A, then show that
P(x*y,A) ≥ P(x,A)+P(y,A)-1

(In reply to

Part 1 by Jer)

Its obviously true,if x and y are primes and x*y=A.

You have taken that case only and that too 4=2+3-1.

*Edited on ***July 17, 2007, 5:51 am**