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How do you check if your regression parameters are significant? Given a number's prime number decomposition, how many ways are there of factorizing it into two different factors?

3 Answers

answer to prime number question: I am assuming that the 2 factors you factorize it into are relatively prime, in that they have no common factors. For a number N, suppose it is represented as a product of prime number N=\Pi_i p_i^(e_i), where p_i is a prime number and e_i represents the number of such primes in N's prime number factorization. For N=xy, we see that for each p_i, we can choose whether ALL p_i factors go to x or go to y (2 choices). it cannot be that we take some of the p_i factors and give them to x, then give the others to y because otherwise x and y will have common factors. Thus, for each p_i we have 2 choices as to where it can go: x or y. So nominally we have 2^n possibilities. However, since (a)(b) and (b)(a) are considered the same factorization, we over count by a factor of 2, so really we have 2^(n-1) possibilities.

regarding my above answer: the upper limit on the product \Pi should be n. That is, \Pi_{i=1}^n

your assumption of relatively prime makes the problem easy...i don't think that's the goal...try to answer the actual question without making sweeping assumptions!!

What is the expected number of coin tosses required before 3 heads in a row show up?

2 Answers

Definition of eigenvalues/eigenvectors. Requirements for stability of a dynamical system.

2 Answers

What is d x^x/dx?

2 Answers

What is a 'pure virtual function'? - Was the only difficult one for me as I am not as familiar with C++ as other languages. :/

1 Answer

A reasonably easy question about sorting lists.

1 Answer

find declarative algo from recursive one

1 Answer

You have a scale and 18 balls. One of the balls is slightly heavier than the rest. The rest are identical. What is the minimum number of times you need to use the scale to determine which ball is the heavy ball?

1 Answer

About market risk methodologies and procedures

1 Answer

Typical interview questions - tell me about yourself

1 Answer
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