ფაილების კატალოგი

Definition. For a positive integer n, the poi of n, denoted poi(n), is the product of the indicators in the canonical disintegration with the prime divisors of the n.
For example:
poi(1)=1,
poi(2^4)=4,
poi(2*5*13)=1,
poi(2^3*5^12*23^6)=3*12*6,
poi(2^4*7^4)=4*4.

Conjecture 1. (Papava). If a+b=c>2 and gcd(a,b)=1 then
c<rad(abc)poi(abc).

Conjecture 2. (Papava). If a+b=c and gcd(a,b)=1 then
poi(abc)≤rad(abc).