SOLUTION: If a ≡ -25 (mod 7) then a is equal to

Question 1205221: If a ≡ -25 (mod 7) then a is equal to
Found 4 solutions by MathLover1, math_tutor2020, ikleyn, greenestamps:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
≡
What is the remainder when you divide by ?
≈ => round it to

then

the answer is:

Answer by math_tutor2020(3821)   (Show Source): You can put this solution on YOUR website!

The closest multiple of 7 to 25 is 28
Add it to -25 to get 28+(-25) = 28-25 = 3

Therefore 3 = -25 (mod 7)
Both 3 and -25 give the same remainder when dividing over 7.

Answer by ikleyn(52946)   (Show Source): You can put this solution on YOUR website!
.
If a ≡ -25 (mod 7) then a is equal to
~~~~~~~~~~~~~~~~~~

                    The question is posed FATALLY INCORRECTLY,
        showing that the "composer" does not understand the meaning of words.

If a ≡ -25 (mod 7), then we CAN NOT say to which number "a" is equal to. We only can say that a ≡ -25 (mod 7) is the same class of integer numbers as a ≡ 3 (mod 7) . In other words, we only can say that if a ≡ -25 (mod 7), then "a" has the remainder 3 when is divided by 7.

Fixed, solved, answered in a right way and fully explained.

Answer by greenestamps(13219)   (Show Source): You can put this solution on YOUR website!

As the problem is presented, there is no way to know what a is equal to. By the definition of mod, a can be any number that differs from -25 by an integer multiple of 7.

The usual intent of a problem like this is to have the answer equal to a non-negative number less than 7.

So a typical correct presentation of the problem, allowing a single answer, would be something like this:

"Solve: a ≡ -25 (mod 7) (0 <= a < 7)"

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