# Find Integer Solutions for (A+3B)(5B+7C)(9C+11A)=1357911

• MHB
• anemone
In summary, the problem asks to find integer solutions for the equation (A+3B)(5B+7C)(9C+11A)=1357911, where A, B, and C are integers. Integer solutions, which are whole numbers without fractions or decimals, can be found using trial and error or algebraic methods. There is no specific method or strategy for finding these solutions, and the values of A, B, and C can be any integer as long as they make the equation equal to 1357911.
anemone
Gold Member
MHB
POTW Director
Find all integer solutions (if any) for the equation $(A+3B)(5B+7C)(9C+11A)=1357911$.

I would start by finding the prime factors of 1375911 (there are five) then forming all groups of 3 factors.

Hi HallsofIvy!

Thanks for your reply. But since this is a challenge question, I hope you know our expectation here is to receive a full solution, no more, no less. (Happy)

No solution because

RHS is odd so all factors are odd so each term in the LHS is odd. there are 3 terms on the LHS and so their sum has to be odd.

but sum is 12A + 8B + 16C which is even so impossible

## 1. What is the purpose of finding integer solutions for this equation?

The purpose of finding integer solutions for this equation is to determine the values of the variables A, B, and C that satisfy the equation and make it true. This can help in solving real-world problems or understanding mathematical concepts.

## 2. How do I find integer solutions for this equation?

To find integer solutions for this equation, you can use a variety of methods such as substitution, elimination, or graphing. You can also use online tools or computer programs to solve the equation.

## 3. Can this equation have more than one set of integer solutions?

Yes, this equation can have multiple sets of integer solutions. In fact, there are infinite possible combinations of A, B, and C that can satisfy the equation and make it true.

## 4. Are there any restrictions on the values of A, B, and C in this equation?

Yes, there are some restrictions on the values of A, B, and C in this equation. For example, the variables cannot be negative since the equation only deals with positive integers. Additionally, the values of A, B, and C should be within a certain range to satisfy the equation.

## 5. Can this equation be solved without using integers?

No, this equation specifically asks for integer solutions. If you use non-integer values for A, B, and C, the equation will not hold true. However, you can use non-integer values to approximate the solutions for this equation.

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