Find Sum of 4 Different Natural Numbers with $(7-m)(7-n)(7-p)(7-q)=4$

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  • Thread starter Albert1
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In summary, the equation for finding the sum of 4 different natural numbers is $(7-m)(7-n)(7-p)(7-q)=4$, where m, n, p, and q are the four different natural numbers. To determine if a set of four numbers satisfies the equation, you can substitute different values for m, n, p, and q and check if the result is equal to 4. The equation only works with natural numbers and the order of the numbers does not affect the result. The number 7 is used as a constant in the equation and serves as a placeholder for the four different numbers.
  • #1
Albert1
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$m,n,p,q\in N$
$m\neq n\neq p\neq q$
and $(7-m)(7-n)(7-p)(7-q)=4$
find:$7m+7n+7p+7q=?$
 
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  • #2
Albert said:
$m,n,p,q\in N$
$m\neq n\neq p\neq q$
and $(7-m)(7-n)(7-p)(7-q)=4$
find:$7m+7n+7p+7q=?$

let 7-m < 7-n < 7-p < 7- q without loss of generality

product of 4 different numbers is 4 so they are -2,-1, 1 , 2

so 7-m + 7-n + 7- p + 7- q = 0 or m+n+p+q = 28

so 7m + 7n + 7p + 7q = 196
 

Related to Find Sum of 4 Different Natural Numbers with $(7-m)(7-n)(7-p)(7-q)=4$

1. What is the equation for finding the sum of 4 different natural numbers?

The equation is $(7-m)(7-n)(7-p)(7-q)=4$, where m, n, p, and q are the four different natural numbers.

2. How do you know if a set of four numbers satisfies the equation $(7-m)(7-n)(7-p)(7-q)=4$?

You can solve the equation by substituting different values for m, n, p, and q. If the result is equal to 4, then the set of numbers satisfies the equation.

3. Can a set of four numbers with decimals or negative numbers satisfy the equation $(7-m)(7-n)(7-p)(7-q)=4$?

No, the equation only works with natural numbers, which are positive whole numbers starting from 1.

4. Is there a specific order in which the numbers should be arranged in the equation $(7-m)(7-n)(7-p)(7-q)=4$?

No, the equation is commutative, meaning the order of the numbers does not affect the result.

5. What is the significance of the number 7 in the equation $(7-m)(7-n)(7-p)(7-q)=4$?

The number 7 is used as a constant in the equation to ensure that the result is always equal to 4. It is also a part of the natural number series and serves as a placeholder for the four different numbers in the equation.

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