How many pairs of positive integers (A and B) exist?
The task is to find the number of pair of positive integers (a, b) which satisfy the equation for given n and m. Only one pair (3, 0) exists for both equations satisfying the conditions. There are no such pair exists. Recommended: Please try your approach on {IDE} first, before moving on to the solution.
How many ordered pairs satisfy the equation 1/x + 1/y = 1/n?
Given a positive integer N, the task is to find the number of ordered pairs (X, Y) where both X and Y are positive integers, such that they satisfy the equation 1/X + 1/Y = 1/N. Explanation: Only 3 pairs { (30,6), (10,10), (6,30)} satisfy the given equation. Recommended: Please try your approach on {IDE} first, before moving on to the solution.
How many pairs of numbers exist for both equations satisfying the conditions?
Only one pair (3, 0) exists for both equations satisfying the conditions. There are no such pair exists. Recommended: Please try your approach on {IDE} first, before moving on to the solution. The approach is to check for all possible pairs of numbers and check if that pair satisfy both the equations or not.
What is the remainder when N2 is divided by (Y – N)?
Solve for X using the given equation. Therefore, it can be observed that, to have a positive integer X, the remainder when N2 is divided by (Y – N) needs to be 0. It can be observed that the minimum value of Y can be N + 1 (so that denominator Y – N > 0) and the maximum value of Y can be N2 + N so that N 2 / (Y – N) remains a positive integer ≥ 1.
How do you prove that there is no integer b?
If f is a polynomial with integer coefficients such that there exists four distinct integer with �(��)=�(��)= �(��)=�(��)=����, then show that there exists no integer b, such that f(b)
How do you show that a positive integer is good?
Show that a positive integer n good if there are n integers, positive or negative and not necessarily distinct, such that their sum and product both equal to n. then |a|+|b|+|c|+|d| Example 8 is as good as =�×�× �.�.�.�(−�).(−�)=�+�+�+�+�+ �+(−�)+(−�)=� Show that the integers of the form (4k+1) where k ≥� ��� �� (�≥�)are good. 21.