# How do you find the integer solution?

Table of Contents

## How do you find the integer solution?

Let a,b∈Z with a≠0.

- If a divides b, then the equation ax=b has exactly one solution that is an integer.
- If a does not divide b, then the equation ax=b has no solution that is an integer.

**What is the sum of positive integers p for which the value of 13 p2 3 is a positive integer?**

13/(p^2-3) to be a positive integer p^2 – 3 must be a (positive) factor of 13. Since we need the sum of only positive value of p, then the sum is 2 + 4 = 6. Answer: D.

### How do you justify a solution?

To justify a solution, students will need to be able to use appropriate mathematical language to give reasons for the particular approach used to solve a problem. Any time that a student produces a ‘solution’ in an attempt to solve a problem, that ‘solution’ needs to be justified.

**What is integer solution for a linear equation?**

The notion of “general integer solution” of a linear equation with two unknowns is extended to linear equations with n unknowns and then, to linear systems. The properties of the general integer solution are determined (both of a linear equation and of a linear system).

## What are the possible values of remainder r when a positive integer is divided by 3?

The values of remainder r when a positive integer a is divided by 3 are 0 and 1 only.

**What are the two consecutive even integers whose squares have sum 340?**

∴ The two consecutive even integers are 12 and 14.

### How do you write a justification statement?

How to Write a Justification Narrative

- State Your Claim. A strong justification narrative begins with a brief statement of your claim, which will be the focus of your piece.
- Establish Reasons. Once you state your claim, begin providing the reasoning.
- Provide Support.
- Discuss Budgetary Issues.

**How do you write justification in math?**

justify why each step in the process of solving a linear equation is legal! The justification method shown above is an example of one method….

Steps: | Justification (Reasons): |
---|---|

x(3 + 5) – 6 = 9x – 24 | Distributive Property in reverse |

x(8) – 6 = 9x – 24 | Addition |

8x – 6 = 9x – 24 | Commutative Property of Addition |

## How do you solve linear congruence?

Generally, a linear congruence is a problem of finding an integer x that satisfies the equation ax = b (mod m). Thus, a linear congruence is a congruence in the form of ax = b (mod m), where x is an unknown integer. In a linear congruence where x0 is the solution, all the integers x1 are x1 = x0 (mod m).

**What are the value of remainder r when a positive integer?**