_{}
- How many pairs of positive integers x and y satisfy the equation xy = 20132013 ? How many pairs ofpositive integers x and y satisfy the equation xy = 20122012?
Look at this webpage.
It tells you that there are 24 divisors. So what is the answer?
If you are talking about ordered pairs (x, y) such that xy = n, then their number equals the number of divisors of n, which is denoted by d(n) or $\displaystyle \sigma_0(n)$. According to Wikipedia, if $\displaystyle n=\prod_{i=1}^r p_i^{a_i}$ for prime $\displaystyle p_i$'s, then $\displaystyle d(n)=\prod_{i=1}^r(a_i+1)$.
How many pairs of positive integers x and y satisfy the equation x^y = 2013^2013 ? How many pairs of positive integers x and y satisfy the equation x^y = 2012^2012?
Sorry, I think I didn't make the question clear...
How many pairs of positive integers x and y satisfy the equation x^y = 2013^2013 ? How many pairs of positive integers x and y satisfy the equation x^y = 2012^2012?
Sorry, I think I didn't make the question clear... It not just divisor.